What was the first prehistoric animal to be given an official scientific name?

Not necessarily the first one discovered. Mosasaurus hoffmannii was discovered in the 1760s but wasn’t officially named until the 1820s.

Some fossil mammal names (Megatherium americanum, Ursus spelaeus, Mammut americanum) date back to the 1790s. Were paleontologists naming species before then?

Yup. Linnaeus himself published work on the trilobite in 1759:

Dunno if there’s an earlier example, though.

It goes back at least to 1758, the year that Linnaeus applied his binomial system to animals. He described at least one fossil snail this year (the name has since been changed).

The year 1758 is recognized as the official start date for binomial nomenclature for animals, so there won’t be any official names that are earlier. However, certainly Latin names had been applied to fossils earlier.

Ironically, the ICZN ruled to suppress “Entomolithes paradoxus” in favour of its junior synonym Paradoxides paradoxissimus, for the reason explained here.

Any ideas on the oldest currently valid taxonomic name for a fossil, or the oldest applied to a vertebrate?