is koichi the name of a company?
No, he is a video game designer.
Koichi Ishii
sometimes credited as Kouichi Ishii, is a video game designer perhaps best known for creating the "Mana" series (known as "Seiken Densetsu" in Japan). 
what is 'trials of mana'? An action role-playing game. who designed this game? Koichi Ishii.
wiki:11068466
Koichi Ishii [SEP] Introduction
, sometimes credited as Kouichi Ishii, is a video game designer perhaps best known for creating the "Mana" series (known as "Seiken Densetsu" in Japan). He joined Square (now Square Enix) in 1987, where he has directed or produced every game released in the "Mana" series (as of 2006). He has also contributed to several games in Square Enix's "SaGa" and "Final Fantasy" series, and created the well-known chocobo and moogle characters.