Hello hello! Seungmin revealed it in the 191008 Twitter Blueroom Q&A that he in fact already had an English name (same with Hyunjin as Sam, and Han as Peter). Presumably, they got their English/Anglicized names because of living somewhere Korean names may be hard to pronounce, such as in LA for Seungmin, Las Vegas for Hyunjin, and Malaysia for Han.
Chan did (jokingly) suggest other members names though, like Bartholomew because it's legitimately hard to pronounce :rofl:
https://twitter.com/bunn1j0o/status/1615141219457466370

In Seungmin's 200227 vlive, he also said the name Sky was chosen because looking at the sky makes you feel good... :face_holding_back_tears:
https://twitter.com/seungmiko/status/1234623292331450369