What's the name of the liver test that they run before they'll prescribe Paxlovid?

They should look for the AST and/or ALT (aka SGOT, SGPT) and possibly Bilirubin. Those can be found in your comprehensive metabolic panel, but it also checks over 20 other things. Some of which may come back irrelevantly & inconsequentially abnormal, which is why it is often best to just get the individual tests needed.