Numbers.
There are certain teams I ID by name but there are numerous cases of name overlap in FIRST (anything that begins with Robo or Techno are the usual suspects). I went to Buckeye a few years ago and we had three Robotcat teams at the event alone!
Ironically due to my involement in FIRST it has helped me memorize combinations better by thinking of which FIRST team the numbers are assoiated with and then the name. My old combo for my office was Grasshoppers. Red Barons.
Personally, I go mostly by team numbers, although there are a few teams I also know by name. As an inspector, it’s really the only way to keep everything straight. Besides, it’s also the easiest way to find teams, since they’re usually laid by number in some pattern.
I had a hard time picking - and maybe I picked wrong.
Some teams I know more by name, others by location, others by number. I guess my answer is the time honored, “It depends …”
And you forgot one of my favorite methods - team shirt. I was checking in teams before alliance selection one time and I was marking off numbers just by looking at the shirts. You know you’ve been around FIRST too long when …
Not quite–343 (Metal In Motion) is from Seneca, South Carolina. 
Though it’s funny you put our digits that way–this year, we (2815, Los Pollos Locos from Columbia, SC) shared Archimedes with 2851 (Crevolution, from Sterling Heights, MI). Never has an alliance selection been more painful for us than hearing “Teams 2590 and 1218 would like to invite team twenty-eight-fif-tee…one”.
(And note how Kara refers to the University of South Carolina as USC. We’ll get the world straightened out someday! :D)
Numbers all the way.
When I first started I remembered team names, I hated numbers, I remember coming home to my mom and telling her “thank god my team number is 111, it’s so much easier to remember than 217”. I spent the first year I was on 'Stang learning team names, and then the next year everyone changed their names on me and I had no idea which team was which. Now I just remember the team numbers, followed by their locations.
#!@%$, at least I was on the right side of the country! ::ouch:: Clearly, I’m not as good at this location thing as I like to think I am.
You may have been thinking of 333 or 353! Both are from New York.
Most teams are numbers to me- mostly because when I’m in school and spewing random numbers, I feel like I’m talking in some secret code 
And we wonder why the football team thinks we’re weird…
well then, I guess they’re just another set…
of tools.
YYYYYYYYYYYYYEEEEEEEEEAAAAAAAAAAAHHHHHHHHHHH
For me, I normally use the numbers. It depends though because lately I’ve been looking at team websites so I know them by that. At competitions I remember them sometimes by mascot, and uniform or their chant.
When it comes to Australian teams, its much easier to memories their location, compared to their team location, or (for most of them) their non existent team number (nearly all the teams only attended our off-season event, the Duel Down Under and didn’t register with FIRST). So we know them as “Team Melbourne” or “Team Tasmania” or “The St Mary’s Team” or “The Adelaide Team.”
When it comes to regionals that our team attends in the US, it’s usually team colours that stand out for me. As for teams recognising us, we’re usually just “the Aussies” =P