It's by direct analogy with Transalpine and Cisalpine Gaul (Galla Transalpina and Galla Cisalpina), which were named by, you know, Julius Caesar, in one of his most famous writings

But I'm sure you know more about Latin grammar than he did https://twitter.com/ReginaAtkinson0/status/1290463564499767296

"Transgender" in its modern usage does not mean that the trans person has "changed gender"

It means that their real/internal gender is different from their assigned gender, that the two gender designations are on "opposite sides of the gender line"

Which is the same way we talk about "trans" and "cis" configurations of molecules -- are the functional groups on opposite sides of the backbone or on the same side

It's a fairly neat analogy