Hi Eliza! Good to see you again.
On JSTOR I found an old (1898) article in a journal called T’oung Pao* (v. 9, n. 3); the article is “Geographical Notes: I. The Nicobar and Andaman Islands” by G. Schlegel. The author mentions the following possible etymologies (I can’t copy and paste from these page images, so I will have to summarize)
1) “Andaja mana” (I omit some diacriticals) can mean “egg-laying barbarians” in Sanskrit, but the name probably is not Sanskrit.
2) from Hanuman, the monkey god, but Schlegel considers the interpolation of the d problematic.
At first I thought he had mentioned a third, but on rereading it appears he was just discussing a Chinese name that may or may not refer to the same islands, and if it does, probably derives from “Andaman” rather than the other way around.
*Apparently a major Sinological journal, but not familiar to me (no Sinologist).