If you want the TL;DR version, just skip to the last paragraph.
This question is a bit easier to understand if you're Catholic or are knowledgeable in Catholicism. I'll try my best to help explain this as a Catholic myself. It might be long, but trust me, you will understand Yuuki/Zekken from Sword Art Online 2 a lot more if you take the time to read all of this. First, what is Catholicism? I think it's important knowing so that you understand Yuuki's decisions and thought process in naming her unique 11 hit combo sword skill. This might be a little long, but I think it's important to first give a quick crash course in Catholicism before I explain how it relates to Yuuki.
To start, all who are part of the Catholic Church are Christians. Catholic and Christian are synonymous, they are the same thing. To be Catholic means to be Christian. While there are other denominations of Christianity, it doesn't mean they are Catholics. All Catholics are Christians, but not all Christians are Catholic. Catholic means "universal" in Greek, which is used in Catholicism as representing "Universal Christianity". That is, Catholicism teaches the Christian faith to its fullest and most orthodoxy extent. Catholicism is both the original and oldest branch of Christianity, founded by Jesus Christ in 33 AD (Almost 2000 years old now) when he appointed the Apostle Peter as the first pope to look after his flock (Christians) in His (God's) physical absence. See to Christians, Jesus is God, and while he is no longer with us in the flesh (physical), he is still with us spiritually in the form of the Holy Spirit from the Trinity (Father, Son, and Holy Spirit). Although the trinity can confuse non-Christians thinking it's 3 gods, the trinity actually represents only one God. Christianity is monotheistic, which is the worship of the one and only God. Think of the Trinity as a 3 leaf clover/shamrock, which has 3 leaves, yet is still the one same clover. When a clover has 4 leaves, the 4th leaf is considered luck, which is where the belief in lucky clovers comes from.
Moving on, I think it's best to explain the Virgin Mary and the rosary now, which is called "Rosario" in Spanish. The Virgin Mary is very important to Catholics because she gave birth to God in the flesh, Jesus Christ. Mary is special because she was picked by God to give birth to Him in the flesh (Jesus Christ, the Son part of the Trinity). Mary then gave God permission to allow her body to give birth to God incarnate, Jesus Christ. I know, that may seem very shocking to non-Catholics, but Christians believe it to be true based on many miracles and many eye witness accounts as proof to Jesus' divinity as God in the flesh. Not to mention that Judaism (Jewish faith) prophesied this thousands of years before the birth of Jesus Christ. Christianity is the continuation of the Jewish faith. Mary's role in Christianity is to help guide all Christians towards her son and Lord, Jesus/God. Catholics consider Mary the ultimate saint, a one of a kind saint whose body was completely pure of any taint of evil/corruption, which was the perfect vessel to give birth to God in the flesh (God's human physical form). That is, Mary's body had the unique trait that allowed God to be reborn into his own creation. This is where the Rosary (Rosario) comes in.
The Rosary is used by Catholics as a form of prayer to recite the "Our Father" and "Hail Mary" prayers. The prayers that comprise the Rosary are arranged in sets of ten Hail Marys, called decades. Each decade is preceded by one Lord's Prayer and followed by one Glory Be. During recitation of each set, thought is given to one of the Mysteries of the Rosary, which recall events in the lives of Jesus and Mary. Five decades are recited per rosary. Other prayers are sometimes added before or after each decade. The crucifix represents the start of this 1+10 combo which results in 11. Rosary beads are an aid towards saying these prayers in the proper sequence. While the rosary form of prayer is not required to be a Catholic, it is encouraged.
Now we finally made it, time to explain how all that represents Yuuki's/Zekken's "Mother's Rosario" unique sword skill. In Catholicism, Mary is considered every Catholic's mother, and she is a huge part of the Rosary. If you combine this fact, you get "Mother's Rosario". One could also argue it has to do with Yuuki's mother, who we find out prayed for her family, especially her children, as evident by the flashback when Yuuki and her mother prayed in a church. Considering the mother was Catholic, it's extremely likely she prayed often with a rosary, making sense of the skill name being called "Mother's Rosario". However, there is actually more meaning to the entire "Mother's Rosario" arc in Sword Art Online 2. Remember how in one of the episodes Yuuki said she did not understand her Catholic/Christian religion when she was younger (shown in a flashback while she's praying in a church with her mother)? Well, that is very common among children in Catholicism since it is very complex. We grow to understand it more as we get older. While some come to understand their Catholicism from an intellectual level by doing tons of research through books and epistles of the Church, many others learn through the Christian concept of suffering. See, Christians believe that suffering has the potential to create good in some form that we cannot perceive at first glance with our limited human intellect. When we suffer, we often question the negative aspects of suffering, but sometimes, we are blessed by it after in some form. As an example, we'll use Yuuki's suffering, who contracted the HIV virus, which then formed into AIDS. This is shown during Yuuki's last few minutes before her death, when she says she finally understands why she went through all that suffering. In Yuuki's case, it was to experience "Love", true love in its purest form, but also to teach others how to love before her death. Also, remember that Yuuki and the Sleeping Knights (her guild where all members are terminal patients in real life) had a deep desire to immortalize their guild and name's in Aincrad's Monument of Swordsmen. The entire guild's suffering empowered them to achieve something that was deemed impossible by most players in the game. Now, that is not saying that Yuuki's suffering is a good thing, because it's not, in fact it's horrible! But her suffering did bless her to be loved and in return to love others, as well as give her the power to endure, yet enjoy her last moments of her life through in-real-life and in-game accomplishments. That is the meaning of the Christian concept of suffering. Another form of blessing from sufferings came after her death, in that Yuuki gave her guild mates of the Sleeping Knights hope and courage to fight their disease, where we are told that Shi-eun and Jun are recovering from their illnesses. Another blessing comes in the form that Kirito and Asuna figure out that Akihiko Kiyaba and his wife are behind the medicuboid technology, suggesting/implying that Kiyaba's reason to create the death game of Sword Art Online was to give Medicuboid technology a jump start for investors to take it serious in order for its technology to benefit mankind in the long run. Finally, Yuuki's suffering leads her to determine who she will pass on her "Mother's Rosario" to. She picks Asuna as its next wielder, to which Asuna tells Yuuki she will make sure the "Mother's Rosario" skill will be passed on to worthy players until the end of time, essentially becoming another unforeseen blessing, her "Mother's Rosario" becoming another permanent piece of evidence that she existed, essentially becoming another action immortalizing Yuuki again in some form. Keep the thought of being "immortalized" on your mind because I will mention it one final time at the end of all of this. Now, the rosary (Rosario) is a 10 + 1 = 11 part of the Catholic rosary. The 10 represents the "Hail Mary" and the 1 represents the crucifix. Does this sound familiar yet? It should, it is a reference to Yuuki's 11 hit combo! Yuuki tells Asuna she named the 11 hit combo unique sword skill "Mother's Rosario" and that it will keep her safe when she needs it. This represents the "Hail Mary" prayer, which is known to be used during difficult or dangerous situations. The "Hail Mary" is a prayer requesting the Virgin Mary to intercede for us in asking for Jesus/God's help when we need Him most. This is the popular football play in the NFL, when player's go for an all-in difficult long throw, the famous "Hail Mary" pass. Makes sense right? Well now, think about when Yuuki uses it. Notice Yuuki only uses her 11 hit combo, "Mother's Rosario", when she is being overwhelmed by a skilled opponent, as evident to only using it against Kirito and Asuna when they managed to briefly overpower her. Yuuki's "Mother Rosario" is her "Hail Mary"! How cool is that?!?! Lastly, I said I would mention "immortalize" one last time. Yuuki is a Catholic Christian, meaning she believes in an afterlife after death. Christians believe in heaven, where they will be granted life everlasting in paradise, essentially immortality in a perfect body, without pain nor sadness, while living in peace and tranquility. Yuuki is looking forward to seeing her family again after her death, and during her dying words, she mentions that she is looking forward to the day that she gets to see all her friends again when they pass into the afterlife like her. This is overwhelmingly a Catholic Christian belief. Even if one is not a Christian, the Catholic Church teaches that even non-Christians have the potential to be granted entry into heaven by God, through the concept of "absolute ignorance". Briefly, "absolute ignorance" basically means non-Christians that are allowed into heaven because of reasons in life that prevented them from learning about or accepting Christianity before the time of their death. This means that all the Sword Art Online characters have the potential to be bound for heaven, even if they're not Catholic/Christian. Yuuki takes her last breaths in life smiling, acknowledging that her suffering lead her to these moments and realizations; lastly ending by saying that she gave it her all and that she was alive.