Sure you can...have a neighbor order the test which you give 'em cash for, pay with his /her credit card, you take the test by spiting in the tube, fill in any name you want and send it in. Close to zero chance they can identify you unless your neighbor rats you out.
It’s not really anonymous though. The neighbors name is attached to it.
It would be nice if they let you do it anonymously but I think they all require you to give your name. Not sure if it’s legal not to. I suppose they want to make sure that you’re not snooping on someone else’s dna.