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

Doesn't that fit Bell to some extent

What Bell is known for, or rather refered as since he doesn't has a reputation for it, is being an Ox Slayer, not a Monster Slayer. His fighting ability is only destacable against Minotaurs not monsters in general. So no, not really.

Many characters are refered to as "the greatest hero" in myths and it is an usual thing for anime characters to want to and/or be heroes, as well as becoming the best. So it only ammounts as another coincidence at most.

slayer of monsters that other adventurer's even a higher level have a hard time battling

Bell has only been able to beat strong monsters due to his ability to reach a high place in the power scale, not because of being particularly suited or skilled at fighting monsters unlike Ais, who is someone who actually specializes in killing monsters.

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

Not everything has to have a deep meaning. Just because Oomori bases a large part of the serie in mythology means everything in it will be a reference to mythology.

We are already 17 volumes in the story (only counting the main serie), it has been well over 8 years since the start of the serie and we have already reached past halfway of it.

If Oomori had actually intended his main character to be based in a mythological figure he would had made a connection way clearer than one as vague as you are proposing, just two coincidences, one of which one is the former's name being part of the latter's.

Considering there has never ben a single reference to Bellerophon, or any mythology character for the matter, regarding Bell and the occasional jokes with his name regarding bells it is clear Bell's name is just because of bells and has no deeper meaning to it.

If your basing this off his name and link to Zeus I should point out that Zeus isn't always his father in the Greek myths he has been link to both Apollo and Poseidon based in the area, and I doubt it sense he was extremely arrogant in the myth to the point that he tryed to fly to Mount Olympus and "take his place as a god" and was killed for it when eather Zeus hits him with a bolt of lightning or Pegasus bucks him off bell is humble to a falt then there's the fact that bell is a close quarters fighter wall in the myths Bellacorn was a rider and long range fighter type