Did you get the info about the supposed alias? IMHO, you should have that for future reference. This may not be the last job you ever apply for, after all.
Yes, you should.
You should find out what the alias is (e.g. “Emilio J. R. St. James McDuncan-Schnieder, Jr.”) as well as what records, if any, are attached to that name.
You should also find out what it was that gave them the pause - was it simple suspicion of failure to reveal a former moniker (and where they wouldn’t have cared if you had revealed it in advance), or does the alias have a checkered history of antisocial behavior and general assholery?