Is this assumption made based on the first four letters?

There is nothing similar to the legends about Bellerophon + it is not a great idea to associate greeks mythology with Danmachi. A lot of people wrote this already, but I'll repeat this - most of all heroes and gods in greeks mythology are real assholes and have nothing in common with the description of the HERO as it is known right now

Was only a though, but aren't many people already names after famous people in mythology, so this does have some base in it, it's not completely impossible, but I see your point

That many characters are named after mythological characters doesn't mean everyone has to, and that also goes for the protagonist.

If the names were more similar and they had actually something in common then it could be a possibility that Bell was named after Bellerophon. However, as that is not the case it is just a mere coincidence, if it can even be called one.

But that hero is famous for being the greatest hero and slayer of monsters, alongside Cadmus and Perseus, before the days of Heracles

Doesn't that fit Bell to some extent, greatest hero and slayer of monsters that other adventurer's even a higher level have a hard time battling, and if Bell is destined to kill the OEBD, then this is fitting

I'm not saying this is a fact, but it seems pretty clear that if Bell is all to Bell's name, then the intent was for it to have this as a secret meaning or something, at least in my opinion