h₃neh₃-mn̥-₂
“named one, having a name”anonymous, pseudonym, synonym
Extended form giving Greek onoma/onyma, English anonymous, pseudonym, synonym, antonym.
Discussion
The PIE form *h₃neh₃-mn̥- (named one, having a name, designated) is a participial derivative of the root underlying *h₁nómn̥ (name), formed with a suffix marking possession or attribution. The form encodes the concept of naming as identity-conferral — to be named is to have social existence.
The base root *h₁nómn̥ (name) is itself one of the most perfectly preserved PIE nouns: Latin nōmen, Greek ónoma, Sanskrit nā́man-, Old English nama, Old Irish ainm, Old Church Slavonic imę — all continuing the same word with clockwork regularity. The derivative *h₃neh₃-mn̥- extends this into the participial domain: not the name itself but the state of being named.
Latin nōmen gave English: nominal (pertaining to a name), nominate (to name for office), denomination (a naming-down — a classified group), pronoun (prō-nōmen, standing for a name), ignominy (in-nōmen, "namelessness" — disgrace, loss of good name), and nomenclature (nōmen + calāre, "name-calling" — a system of names).
Greek ónoma (with regular Greek metathesis from earlier *ónmn̥) gave: anonymous (without a name), synonym (same-named), antonym (opposite-named), pseudonym (false-named), homonym (same-named), and the suffix -onym/-onymy in all naming-system vocabulary.
The cultural significance of naming in PIE society was evidently profound: a name conferred identity, and to lose one's name (ignominy) was to lose social standing. The PIE speakers who reconstructed a participial form for "having been named" encoded the concept that personal identity is a social act — you ARE your name, and to be named is to exist in the community.