How can someone check if their identity has been used in a fraudulent wire transfer?

You honestly cannot. If your name &/or credentials have been used for a fraudulent money wire transfer that is not originating from your account, it becomes next to impossible to check.

If the origination is from your account, that should be obvious, considering the withdrawal (drawdown) from your account.

One of the most significant sources in the world for fraudulent credentials is photocopying (xerox) machines, which have an internal memory and can store whatever is being copied. Be cognizant of where you give your government-issued documents to be copied/xeroxed, etc.