Bain is a noun used as a surname or place-name in various cultures; in English contexts it can refer to a family name or a historical/fictional figure. It is pronounced with a long a vowel, rhyming with
Bain-Marie
How to Pronounce Bain-Marie
Baird
How to Pronounce Baird
Bairn
How to Pronounce Bairn
Bait
How to Pronounce Bait
Baize
How to Pronounce Baize