Is the festival Beltane named for an Irish god Bel?

Short answer: probably not.

The Keltic peoples of the Continent knew of a god Belenos (attested in various spellings) who, during the Roman period, was identified with Apollo.

Belenos clearly = *bel-, “shining, bright” + infixed -n-, (denotes lordship, mastery, or preeminence) + -os, (masculine singular ending). The “mastery infix,” interestingly, features in the names of a number of Keltic deities: among them Cernunnos, “Horned Lord” or “Preeminently Horned” and Epona, “Lady Horse” or “Preeminent Horse.” So Belenos is “Bright Lord” or “the Preeminently Bright.”

Did the Keltic-speaking peoples of Britain know such a god?

If so, the evidence is minimal, and there's none whatsoever that the Irish knew him. ('Beltane' is an Irish word in origin.) We cannot assume that the Insular Kelts worshiped every god that their Continental kin did.

So alas, Beltane is probably not “Bel's fire.”

From his name and association with Apollo, it's often assumed that Bel was the Irish sun god, but since the Irish word for “sun” (grian) is feminine in gender, this doesn't seem likely.

Apparently Bel was brought to us by the same “there's a pagan god hiding behind every standing stone” school of 19th-century scholarship that brought us Samhain, the Druidic lord of the dead. (Samhain, being yet another feminine noun, would have been a goddess if she had been a deity at all; but there's no evidence that she was.)

Bye-bye Bel.

Sure, and Bel-fire would have made a nice pairing with Lughnasadh, “Lugh-assembly,” but the evidence (such as it is) suggests otherwise.

In all likelihood, Beltane originally meant “shining fire” or “bright fire.”

Which (let it be said) ought to be quite good enough for anyone.

One thing at least we can say for certain.

As with Easter and Ishtar, Beltane has nothing whatsoever to do with Ba'al.

Absolutely nothing.