How do you translate “blockchain” and “bitcoin” to Latin?

This won’t be good, for the reasons Alberto Yagos said.

The Greek for bit is: Bit – Βικιπαίδεια. Of course. There is a Hellenic coinage recommended by the Greek Standards Organisation: δυφίο dyphio[n], from dyo “two” and psēphion “digit”. The Ancient Greeks didn’t do portmanteaux, which is what this is; but if you want a Hellenic bit, that’s what’s on offer.

So you *could* go with dyphionomisma, where nomisma is a coin.

But honestly, Bitcoin shouldn’t be translated, not only because it is anachronistic, as Katharina Sikorski argues, but because it s a proper name, not a generic term.

Blockchain? I would do back to literal rendering. Chain of ledgers would be Catena Calendariorum—where a calendarium was not originally a calendar, but a ledger. You could say that the calendarium is virtual, but really, Catena Calendariorum is plenty long already.