I know that the nine-tails exists in many anime series (The notables are Naruto and Pokemon), as well as
His name, Kurama, relating to fox demons across different animes, such as Yu Yu Hakusho.
I also know that the two-tails is adapted from Japanese mythology (The Nekomata, a cat with a split tail).
Does this convention apply to all/most other Bijuu?
The concept of the Nine Bijuu is based off Japanese mythology, although there are some parallels Kishimoto does not follow though completely with the myths.
It seems like Kishimoto is purposely using names with different kanji, but the same pronunciation, such as Kokuou in Naruto is 穆王 (majestic/respectful king), while Kokuou from Hokuto no Ken is 黒王 (black king). For Kurama, the Nine-tails, in Naruto it is 九喇嘛 (9 lamas/high priests), the real life Mount Kurama is 鞍馬 (saddle horse), and in Yu Yu Hakusho 蔵馬 (hiding/ownership/storehouse horse).
Kyuubi: 九喇嘛 (クラマ; Kurama), the Nine-tails, is a reference to the kitsune in Japanese mythology. The name Kurama probably named after the mountain in Japan. It is said to be home of the Tengu God Sojobo and, more importantly, the location where the technique Reiki was first learned. Reiki is the art of using chakra (universal energy) to heal other people. This ties into Naruto's life-giving energy ability he gains after tapping into the nine-tails chakra.
Here is the Wikipedia breakdown of Reiki:
"Reiki is commonly written as 霊気 in shinjitai kanji or as レイキ in katakana syllabary. It compounds the words rei (霊: "spirit, miraculous, divine") and ki (気 "gas, vital energy, breath of life, consciousness"). The ki (better known as Chinese qi or ch'i) in reiki is understood as meaning "spiritual energy; vital energy; life force; energy of life"
Hachibi: 牛鬼 (ぎゆうき; Gyuuki), the Eight-tails, is based off the Ushi-Oni, a sea creature commonly seen with an ox head and the body of another multi-limbed creature. The name Gyuuki (cow demon) is another pronunciation of Ushi-Oni.
Nanabi/Shichibi: 重明 (ちようめい; Choumei), the Seven-tails, is probably based off the rhinoceros beetle which are said to be amongst the strongest creatures on the planet in relation to their own size. The name most likely is a reference to Kamo no Choumei, a 12th century poet who secluded himself on society, took Buddhist vows, and became a hermit living outside the capital. Choumei is most famous for his writings that were mostly about nature and natural events. If you recall from the manga, two of the previously unseen captured Jinchuuriki's were outcasts that were abandoned by their village when Akatsuki came to capture them.
Rokubi: 犀犬 (さいけん; Saiken), the Six-tails, Saiken is based off the turban-shell snail demon, Sazae Oni. The name comes from a compilation of Chinese legends called "In Search of the Supernatural". The Saiken (犀犬) in one of the stories (地中犀犬) is a type of dog-like creature with closed eyes, the size of small dogs, that like underground in pairs (male and female).
Gobi: 穆王 (こくおう; Kokuou), the Five-tails, is a reference to the the hanging horse head demon, Sagari, and the ghost whale demon, Bakekujira. Typically Kokuou translates to "king" (国王) in Japanese, referring to a "lesser king," one below the emperor. The name probably is a reference to the Chinese legend of King Mu of Zhou (周穆王).
Yonbi: 孫悟空 (そんごくう; Son Gokuu), the Four-tails, is a reference to the Satori, an ape-like creature that can read minds. The name Son Gokuu is obviously a reference to the Monkey King in Journey to the West.
Sanbi: 磯撫 (いそぶ; Isobu), the Three tails, is probably based of a combination of the spirit of eaten-turtles that haunt those that harmed it, Suppon no Yurei and/or the amorphous sea monster, Umibozu. Isopu is probably a reference to the shark-like demon sea monster with a barbed tail fin, Isonade.
Nibi: 又旅 (またたび; Matatabi), the Two-tails, is a referenced to the forked cat demon, Netomata. Matatabi is named after the Silver Vine or Cat Powder a plant herb similar to a hardy kiwi vine. Used as a healing herb for cats and affects them in a similar way as catnip. When ground up, it is used in herbal teas and bath salts.
Ichibi: 守鶴 (しゆかく; Shukaku), the One-tail, is a reference to the shapeshifting racoon demon, Tanuki. The Naruto One-tail bijuu shares several tanuki archetypes. One is from the Bunbuku Chagama tale, where a tanuki transforms into a tea kettle. In the series, the One-tail is said to have been sealed within one. Other versions of the taunki tale tell of the shrine priest being a tanuki in disguise, which ties into how the One-tail was supposedly corrupted a Hidden Sand priest. The name "Shukaku" probably refers to the priest of this tale.
The one-tail is based on a Tanuki - However, I don't know anything about a background in mythology.
As you said, the two-tails is based on Nekomata.
The three-tails is based on Isonade.
The four-tails is based on Sun Wukong... and maybe a little bit on this one ;).
Kishimoto said that the five-tails s appeareance is based on a horse and a dolphin...
The six-tails is based on Saiken... That's a chinese Yokai.
The seven-tails - don't know.
The eight-tails is based on Ushi-Oni.
The nine-tails is based on Kitsune.
Jūbi (ten-tails) is another name for Daidarabotchi.
Source is the German Narutopedia.
The only other one I know of is that the Four-Tails' name is Son Goku, coming from the Chinese classical novel Journey to the West. The same name is used in Dragonball and its sequel series for the main protagonist.
The One-Tail may also have some connection, as tanuki (raccoon) are common is Japanese culture/mythology.
The Nine-Tails may be a mixture of Kitsune, but I also know that it is also a mixture of Tamamo-no-Mae, which is a malevolent being through many Asian cultures that has been the downfall of many dynasties and it also eats flesh.
