What about the IRS and employment tax your employer pays going to the wrong tax ID that should be reported to you?
I'm sure in some situations it'd work (1099, physical paycheck, lax process), but it seems like you're just setting yourself up to have to break more laws.
You'd be better off just using your own name and keeping a low profile online.
At least then you'd probably only be in violation of your employment contract.
It's stuff like this that's going to make providing recent bank statements and tax records a more common requirement for hire. :-(