Does the first syllable rhyme with “glow” or with “how”? It is no use appealing to the Hindi for “Little Frog” or anything else, since Kipling confessed to making it up of whole cloth, as I discovered after asking a local Hindi speaker who drew a total blank. The question comes down to what sound Kipling meant to suggest by the spelling “ow,” which is hard to figure out, given that homograph pairs like “row” (quarrel vs. line of something) and “bow” (loopy knot or gesture of deference) straddle the difference in question. I know Disney’s film made the first syllable rhyme with “glow,” but I concede to Disney no authority in the matter whatsoever. I used to have access to an LP phonograph disk of Boris Karloff reading aloud, which would be better as authority, but alas I cannot remember how he pronounced the name.
It actually appears that the way it is pronounced may be different.
The Name Mowgli:
In the stories, the name Mowgli is said to mean "frog". Kipling made up the name, and it "does not mean 'frog' in any language other than the language of the forest."
Kipling stated that the first syllable of "Mowgli" should rhyme with "cow" and is pronounced this way in Britain, while in America and India it is almost always pronounced to rhyme with "go".
Andrew Leach left a comment linking to a Kipling Society web page that says
This list of names, their meanings, and pronunciation, was provided by Rudyard Kipling as an Author's Note for the definitive Sussex Edition of his works (Vol. X11, pages 471-8).
MOWGLI [...] is a name I made up. It does not mean. ‘frog’ in any language that I know of. It is pronounced Mowglee (accent on the Mow, which rhymes with 'cow').