Is there a word or term for one who is obsessed with names?

Solution 1:

The appropriate word or a phrase might depend on the context, that is the sort of piece you are writing. For someone who gives names:

nomenclaturist which redirects to M-W 3rd definition of

nomenclator:

3: one who gives names to or invents names for things

Nomenclator is also a book that contains names or lists of words (and most examples of usage refer to this meaning); in the sense that we need here there are more examples of usage* for nomenclaturist:

The aspiring taxonomist or nomenclaturist used to have little choice but to become an obsessive-compulsive book and reprint collector, and had to visit major libraries in large cities on a regular basis to consult rare and obscure books and journals that survived in only a few of the larger depositories.

From: Marine Algae: Biodiversity, Taxonomy, Environmental Assessment, and Biotechnology edited by Leonel Pereira, Joao Magalhaes Neto

If you need someone who coins and deals with technical terms, ODO gives this example of usage for a

terminologist

The terminologist drafts definitions and recommends the adoption of new terms for standardization purposes.

Since giving names is often tied with classification, another appropriate word might be:

taxonomist who is not just someone interested/working in the field of:

the classification of something, especially organisms (ODO)

but also someone who created a tag used by 50 questions on SE (and a tag is a sort of a label, so our taxonomists create labels and assign them to posts).

To convey the obsession or extensive work in the field of name-giving you might need either a neologism or a phrase:

The Name Giver is how National Geographic refers to Carl Linnaeus, describing not just his vast contribution to plant nomenclature and taxonomy, but also a situation from his family:

The child's father, Nils Linnaeus, was an amateur botanist and an avid gardener as well as a Lutheran minister, who had concocted his own surname (a bureaucratic necessity for university enrollment, replacing his traditional patronymic, son of Ingemar) from the Swedish word lind, meaning linden tree.

So the art of creating names obviously ran in the family there.

Sometimes less is more so an ordinary:

name obsessed might to.

But if you would like to go the extra mile, you might borrow The Philolexian Society's term:

Nomenclaturist General

*beware of the false positives: nomenclaturist can be an adjective derived from nomenclaturism

Solution 2:

"A preoccupation with words or names" is onomatomania, so the word for such a person would be onomatophile or even onomatomaniac.

(This whole discussion might onomatomaniacally autological.)

EDIT: Martha suggests onomast, which is a "real" word in the sense that people other than me use it (if you want to resort to that definition) but does not, I don't think, conveys the idea of obsession. More of a sensible expert.