The short answer is : you were right and chose the best natural-sounding one. And it fits equally well in all your listed examples, places, people or animals.

Here you could alternatively have skipped the verb part with Je recherche le restaurant “Jake’s”, but it’s the second-best choice to me, yours is clearer.

All your three variants (qui s'appelle / qui se nomme / dont le nom est) exist and mean the same, but the levels of formalness (?) are different. “Qui se nomme” or “dont le nom est” are indeed more formal.

Last thing, se nommer is mostly used when refering to people rather than things, so it would be the only variant slightly odd here.