The Latin is pollex. This finger acquired the name, according to the grammarian Ateius Capito, quod pollet—because it is the powerful one.  And it is now these words in the Romance languages:

Italian:  pollice
Spanish:  pulgar
Portuguese: polegar
French:  pouce
Galician:  polgar
Catalan:  polze

Some of the lore about how Romans used thumbs is mysterious. In Juvenal’s third satire, his friend Umbricius talks of the nouveaux riches who

munera nunc edunt et, verso pollice vulgus
cum iubet, occidunt populariter…

¶  They now put on gladiatorial shows and kill to popular acclaim,
when the mob bids it with a turn of the thumb.

This business of thumbs was apparently so familiar that nowhere in literature do we find an explanation of it: and people have argued ever since about whether they turned their thumbs up or down.

And then there is the deponent verb polliceor—I promise. Does that derive from pollex, and refer to an ancient act of contract involving the thumb? Lewis and Short do not think so, but that was the explanation of one of my tutors.

And the Greek word for a thumb? The Greeks did not have a word for it.  δάκτυλος μέγας was the best they could do.

The English thumb is common to all the Germanic languages in various forms, and it means, originally, the fat one.

Another word spelt variously in the Germanic tongues is toe, meaning originally one of ten. But neither Greek nor Latin had a word for it, nor do the modern Romance languages. They are compelled to say digit of the foot.  But French also has orteil, and the others sometimes use punta.

A student once asked how a sophisticated language can lack words so basic. I wondered if that might be a question for an anthropologist.