Other diseases from ticks

I'm not sure there are tests for all of them! There are dozens of strains of borrelia alone that can cause disease in humans. There are multiple strains of bartonella and mycoplasma and rickettsia and babesia. Also lots of viruses (powassan, Epstein-Barr, etc.) and parasites (countless). Tularemia. Brucella. The list goes on. Ticks are gross.

(And these illnesses sometimes are spread by other organisms, too!)

Here's a very partial list from the CDC.
https://www.cdc.gov/ticks/diseases/index.html

The three tick-borne infections you hear most about people treating are borrelia bergdorferi, bartonella henselae, and babesia microti. It's possible to have other strains of borrleia, bartonella, and babesia, and it's possible to have none of the above. A doctor who knows about Lyme and its co-infections can order panels of tests, but no panel covers all of them. Based on symptoms, though, a good practitioner should be able to point you in the right direction. It is possible to treat even if you don't know exactly which strains you are dealing with. Lyme is a clinical diagnosis, meaning knowledgeable doctors will take into account signs and symptoms, not just tests.

And it's a whole other topic, but tests for many of these illnesses are unreliable and controversial, so some doctors won't be concerned about testing you at all.

Add Mycoplasma to the list and Chlamydia Pneumoniae.