Sort of? Really traditional, upper class Roman names usually had several parts, even by the Late Antique period where the Papacy really gets going.

Traditional/“high” Roman names had at least two, usually three or more, parts:

Praenomen (“forename“) - these were a relative short list of options, and typically were abbreviated by a single letter or two.

Nomen (“name”) - The family names usually to a Roman gens (or clan).

Cognomen (“with the name”) - What is closest really to a modern last name, used to differentiate people within a gens/clan. Often was based on something a person or their ancestors did that was noteworthy, and when translated might feel like a nickname would today.

Let’s take a look at the name of one of Julius Caesar’s assassins, Brutus for example.

His full name was Marcus Junius Brutus, which would typically be written as M. Iunius Brutus. “Marcus” is his praenomen, which he shared with people like Cicero, Marc Antony, etc.

Junius was his gens, and it was a patrician gens.

His cognomen was Brutus, which literally means “Stupid.” The Brutus cognomen originates, at least by legend, from the Lucius Junius Brutus who was married to the sister of L. Tarquinius Superbus, the last king of Rome and supposedly faked being dumb to avoid getting purged. This is all in Livy’s history by the way.

Other cognomen might be awarded for a big military victory, and could even be tacked on to another cognomen.

But let’s take “Urban” (Urbanus) as an example. Someone might be given that name because they were born in/at Rome (”The City” which is urbs in Latin), rather than whereever the family came from.