The word "pseudonymum"

Question

I am looking for a Latin word for "pseudonym". My (Finnish–Latin–Finnish) dictionary gives the translation pseudōnymum. However, this word seems to be absent in Lewis & Short, and no Latin word for "pseudonym" can be found. The Latin Wikipedia article about the word mentions sources from the 19th century.

This leads to a couple of questions:

1. How old is the Latin word pseudonymum?
2. What are the classical ways to say "pseudonym"?

My guess is that pseudonymum is too young to be classical, but I have no evidence. I have found some ancient instances of nomen falsum, but I wonder if this is the only expression or the preferred one.

Partial answers are welcome if you cannot provide a full answer to both questions.

Answer 1

The adjective ψευδώνυμος “falsely called” is good classical Greek, so one would expect the corresponding noun to be *ψευδώνυμον (neuter) “a false name”, and as such borrowable into Latin.

The Oxford English Dictionary traces “the Latinate form” pseudonymus to the 17th century.

Answer 2

In addition to family names and given names, if a fourth name is taken it is either a descriptive title. in which case it is agnomen, agnominis; (e.g. Cato Censorinus)

or it is a nick-name, 'cognomen, cognominis.' (Cic.)

cognominati ergo simus, aut cognominatae.

(cognomino -Pliny, Suetonius)

pseudonymus, m. is listed in the 'late, uncouth, and barbaric' section of Ainsworth as a 'false name,' along with pseudomartyrs, pseudobishops, pseudodeacons, and the smelly pseudacorus. No citations.

Smith's 'Smaller English-Latin' 1870/1936, has the following entry:

alias: Phr. Turner alias Powell, *Turner aliter nominatus Powell.

(asterisk * means non-classical)