Solved

Is there a way to change my manager's name?

As the title say, I was wondering if it could be possible to change my manager's name

No, this is not permitted as the game prefers folks use their real name. Exceptions might be made by Jack if you currently aren't using your real name.

To answer a possible question, why are there players with names that aren't real? There are a significant, though small, number of players from iGP's legacy format that allowed players to choose any name they pleased (like mine).

Is there a loophole? Yes. Try to make a Facebook or Google account with the name (if they even let you!) you'd like and try connecting it to your current account to see if it changes it. You could even sign-in with said social media account to create a totally new account with the name you prefer.

I've asked for a name change on one of my accounts before and nobody is interested.