Is there an equivalent to iOS' identifierForVendor for android?
There is the Android Id:
Generating Device-Specific Serial Number
Note that Android is designed so you can't automatically get a full device id. Android even modified a pre-existing part of linux that would have made this possible.
Even better than Android id: your app can request the AUTHENTICATE_ACCOUNTS permission. Then you know the user's Google id. This will be common across all apps and phones the user uses.