A while ago I met a girl who told me a word that was perfect for the project I'm working on, which meant to come up with a new word or subject, or term a word or subject that had not previously been named. Any ideas?

meant to come up with a new word or subject, or term a word or subject that had not previously been named

Putney, welcome to the board. Does your name mean you are from Putney (London UK) or is it like Chelsea Clinton? And is Swope the past of swipe? Don't answer if you think it may incriminate you.
To answer your question:
neologism = noun meaning either a new word, or the coining of a new word. I doubt if the verb is "neologise/-ize" though . I would use "to coin a neologism" or similar. Is there a better verb for this?

Be warned however, Mirriam-Webster gives the secondary meaning of:
"a meaningless word coined by a psychotic"
Rod

or is your name from the Robert Downey (Sr). movie of the early 70's (late 60's)?

a marvelous movie-- a major "ad agency" hires a hip, dude black-- who is hired really as window dressing for the 60's equality movement. then the head of the agency dies-- (suddenly-dramaticaly!) and which point the partner need to elect a new head for the agency-- no one is prepared when it comes time for the vote-- so, each thinking to out do each other, votes for Putney Swope-- thinking no one else will-- and suddenly, the man hired for window dressing is the head of the agency.. -- He starts to institute some radical ideas..

The movie was very funny, played serious with common prejudices, and was at once timely-- and timeless. Like "a gentleman's agreement" or other films/stories of the type-- it was sometimes raw-- and cut to the bone-- but it was also very, very funny!

So putney-- are you a hip dude with an outsized afro--heading an ad agency? or just hip to the way of the world, and trying to change it with humor? --or as Rod suggests, english? or all of the above, or none of the above? or like garbo-- you just want to be left alone?

of troy, you are a never-ending font of knowledge. I'll bet that people will play Trivial Pursuit with you only once.

sparteye-- haven't you yet noticed? great breadth-- no depth! So yeah, i am great at trivia! and I know almost nothing about sports!

So the first time i played trivial pursuit-- i kept on going until i had to answer a sports question-- and my cousins, (all guys) thought "Aha! we've got her how... " and then, wouldn't you know it-- i got one of the six or seven questions about sport i could answer-- and what was worse-- none of the guys knew the answer... (they refuse to ever play with me again)

Q. On what golf course do you have to cross a 13th century stone bridge to play (X)th hole?

A. On St Andrews, in Scotland, of course. It was really a simple question. You knew it had to be old world-- (13th century bridge) and really, what is the most famous golf course out side of US? I don't any other one!