Is there a name meaning "not a singleton"?
Multipleton?</facetious>
A more serious answer: if there is such a term, I've never heard of it; I would just say non-singleton (or even, I dare say, normal/standard/regular :-P) myself.
decepticon.
ahem sorry, sorry.
No there isn't (if you think about it singletons are the extraordinary case), but simpleton was another interesting suggestion.
Multi-Instance ?
http://elegantcode.com/2008/04/17/the-opposite-of-a-singleton/
Castle Windsor uses the term "transient" to describe all non-Singleton objects.
I personally prefer the term "non-Singleton" though.
Actually, there is a variant on the Singleton called Multiton or Multiplton or something like that. Rather than having one instance, you have n instances where n is a specific value. I'm not sure if the Gang of Four describe this application in their book, but I learned about it in my Software Engineering 361 class.
But if you have an unconstrained number of instances, I don't think there is a name for it.
A Marriedton?
I would just call it an Object. The fact that you don't call it a Singleton implies that there may be more than one instance.
Prototype. It is used as a scope in Spring framework to identify dependency which will always be new instance when injected.
When someone asks me if a class is a Singleton (and it isn't), I just say no, it's a regular class.
Yes, there is a Multiton pattern, but it means something very specific. It's not simply everything that's not a Singleton.