The “democrats” (as in democracy) and “republican” (as in a republic) are not very descriptive identifiers for a democratic party in a republic (though I guess you could argue a two-party system isn’t very democratic).
In many other countries, parties are labelled as “Progressive”, “Conservative”, “Socialist”, “Christian Democratic”, “Social Democratic”, etc. that give you some idea of what they stand for / believe in, albeit in some cases, they can be misnomers and be things they want you to think they believe in (e.g. the various “democratic” parties in one-party states). Why are the American parties so boringly named with such broad descriptors?
p.s. Whatever happened to the Bull Moose party?
In Australia our establishment conservative party is called the Liberal party. I understand why and how it actually made perfect sense at the time but man if that isn’t ever ironic in modern context.