Hmm, I always thought the name PC Engine was a rhyme play on PC Genjin (Prehistoric Kid-Bonk's Adventure) since it was the flagship title so to speak.
Close, PC Genjin is a rhyme play on PC Engine.
The character was created after the system as part of a comic strip for a japanese magazine. The comic became popular enough that they slapped a game together which happened to be good/popular enough to get proper sequels.
Whoever was handling the Turbografx over at NEC in the U.S. was smart enough to use Bonk as a mascot, but he wasn't one for the PC Engine.