A Character Named trope should be should only be named for a character who is very well known for exemplifying the trope. This trope is about characters and people who are not well-known because they were no longer in the group or work when it became famous. While Pete Best is only obscurely known as "that drummer the Beatles had before Ringo". Trope namers are supposed to be identifiable, and being obscure means any example of this trope cannot be readily identifiable.
About 6 of 15 wicks (checked so far) misuse the trope, a rate of 40%.
It may be possible to pick a name that indirectly references Pete Best as the trope codifier and by extension similar figures without referring to him by name.
Pete Best is a man who is literally famous for (at the time) not being famous. He -is- the Most Triumphant Example of this trope, at least where music is involved, and his split with the group shortly before they made it big is infamous in the rock and roll fandom. That passes the "in a certain fandom" guideline on "when not to rename". Also, Pete Best passes the One Mario Limit.