I doubt this etymology, are you sure of it? (As the other poster pointed out, your etymology needs a sva->sa change which is rare in most parts of
India that spell the dental unaspirated t as th; though not so rare outside.) What language do you think the name is from? Stated differently, which culture do you think the name comes from?
From the distribution of this name (in
Andra Pradesh and Karnataka, in places historically dominated by a muslim culture), I would have guessed it is a `hindu'-ization of a muslim (persian or arabic) name patterned after ajit. This is, however, a wild guess. It could possibly mean `with victory', though to my knowledge, that compound is not attested in Sanskrit.