Background check for a job reveals someone else may be using my SSN

I (M25, DC) already have a freeze on my experian account, and to my knowledge there’s been no foul play re: taxes or credit lines. From what it looks like, they are in the Atlanta area and have a foreign-sounding name. I’ve never lived in GA, and am not sure what else they’ve been up to, but the background check seems to have passed anyway, even though this persons name has now been listed as an “alias”. The job in question that commissioned this has not contacted me yet since it was only finished today.

What are my options here? The SSA website basically said to just freeze my credit reporting accounts and watch for suspicious activity. Is there anything else I really CAN do? Try and find them myself, give them a stern talking-to? I would hate for this to ruin the offer since it’s not my fault and I’m coming off a few months of unemployment.