Here is a list of all the characters that come out in the manga, and anime.
If you see a line through a characters name like so Misa Amane then they are already taken.
If you see a name in Italics like so they are taken, but you may still apply for them.

Kira
Light Yagami
Misa Amane

NPA
Soichiro Yagami
Shuichi Aizawa
Touta Matsuda
Kanzo Mogi
Hideki Ide
Hirokazu Ukita

FBI
Raye Penber
Naomi Misora
Steve Mason

Mafia Bosses
Rod Ross, real name Dwhite Gordon

Mafia
Jack Neylon, real is name Kal Snydar
Zakk Irius
Glen Humphreys, real name Ralph Bay
Rashual Bid, real name Al Meem
Andrew Miller
Jose
Roy
Skyer

SPK
Stephen Gevanni, whose real name is Stephen Loud
Halle Lidner, whose real name is Halle Bullook
Anthony Rester, real name Anthony Carter
Ill Ratt, real name Shawn Dunleavy
John McEnroe, real name Larry Conners
Ellickson Gardner, real name Ellickson Thomas

Wammy House
L
Near
Mello
Watari
Matt, whose real name is Mail Jeevas
Roger Ruvie

Shinigami
Ryuk
Rem
Shidoh

Allies
Aiber
Wedy
Yitzak Ghazanin

Yotsuba
Kyosuke Higuchi
Shingo Mido
Reiji Namikawa
Eiichi Takahashi
Suguru Shimura
Masahiko Kida
Takeshi Ooi
Arayoshi Hatori

Humans
Kiyomi Takada
Teru Mikami
Hitoshi Demegawa
Koreyoshi Kitamura
Sachiko Yagami
Sayu Yagami