As the topic/question says, what is the meaning if the name of the anime. I want to tell you that I watched the series because of its peculiar name. But after watching the entire series, I could not decipher the relation between name and the series itself! Am I missing something? Surprise me!
I take it to be the main character being thrust into a conflict against his will while also providing him an overpowered power he never really wanted, i.e. his Guilty Crown.
"The right to use my friend as a weapon. That is the sinful crown I shall adorn. I accept this 'guilt.'"
EDIT: Seemed a bit of confusion and adding the detailed comment by Hikari to the answer verbatim.
in guilty crown the protagonist is only able to wield his power by pulling the soul of another person. If he breaks that soul they die and he carries that guilt and shame of not being able to do anything alone. Just like a king may "technically" rule a country but only on top of the shoulders of the people who believe in him and the soliders who die for him. And typical of the shounen genre all of this is thrust on the shy,wallflower like boy with no confidence. That is where the title came from. It is more like an allude as to what the whole series portrays. – Hikari
it could be understood as 'crown' meaning the power that the main protagonist has because someone with a crown is usually the king or queen, in this case, it's a king. he has a lot of power to use and is the leader of the rebellion/survivors as well which would suggest that he is like a king ruling over his people and trying to protect it. 'guilty' is because he uses people's souls and ask people to use their souls for him without telling the people what it will do to them. the person with the glasses (forgot his name) was also hiding the fact that if the soul is destroyed, the owner dies as well and when the protagonist realizes that he feels guilty for everything he's done. and add these together can give you the name Guilty Crown.
Hope this helps