> I was wondering if the patronym "Mac Dear-bháil" might contain the
> element "Bel". Could "Dear-bal" possibly translate as "daughter
> of Bel" or "priestess of Bel"?
That's an astute suggestion, but the authorities (DIL and Ó Corráin
& Maguire) indicate that Derbáil is "Daughter of Fál". "Der" is a
poetic word for "daughter", causes nasalization, and is followed
by the genitive of a noun, so "der + fál = der b[h]fáil > derbáil".
"Fál" is a name of Ireland.
Another name, spelled "Deirbhile" in Classical Modern Irish, is
tantalizing, but derives either from "derbiled < der + filed =
daughter of a poet" or from "der + bile = daughter of a hero (lit.
a great tree)". "Daughter of Bel" would presumably be either
"Derbil" or "Derbeil". NB: the native grammarians and poets
permitted lenition as well as nasalization after "der".
Looking for the mysterious "Bel" in a proper name of a person or
place is not a bad strategy!