Considering that Sebastian was seemingly only given a first name at the beginning of his contract, I would assume that demons choose their own surnames should they become necessary?
Given the etymology of his name, I would guess that Sebastian came up with it when officially fully introducing himself to Tanaka, knowing that the man was Japanese and might pick up on his little bit of word association (since we know that Sebastian is a fan of wordplay).
He also probably had some prior knowledge of the demonology reports of the late Sébastien Michaëlis (1543-1618), which just meant double points for humour and irony - not just to be recognised by himself, but also by the demon Berith who had given over the information, as one of his noted roles in Hell is to officiate demonic pacts as Chief Secretary of Hell and Head of Hell's Public Archives.
Claude meanwhile decided:
"Idk, Faustus, as in Dr. Faustus, as in Faustian Contract...
... I don't really want to be here tbh."