First of all, yes there is a bucket of nametags.
Every park, or area (e.g hotell, downtown disney etc), have a warderobe. If you have forgot your nametag, you have to get one here, in the same way every castmember sign out costumes. So, if you see a castmember with a nametag saying: "pat", ask if that is her/his real name.... (most of those nametags are "pat")
To all You frightend moms:
Check the outfit of the castmember. All castmember have to wear a costume, or a buisness-outfit.
AND take a look at the shoes, they have to be black dress-shoes!
But I dont think you should be worried that there is a "fake-castmember". I have NEVER heard of one...