What you describe (creating new named variables at runtime) is possible in interpreted languages like JavaScript, Lua, Bash, but not with a compiled language like Java. When the loop is executed, there is no source code there to manipulate, and all named variables have to be defined before.
Apart from this, your variables don't need a "unique" name, if you are using them sequentially (one after another), you could just as well write your loop as this:
while (someArbitrarySet.hasNext()) {
SomeClass sC = new SomeClass();
sC.callSomeMethod();
}
If you really need your objects at the same time, put them in some sort of data structure. The simplest would be an array, you could use a Collection (like an ArrayList) or a Map (like CajunLuke wrote), if you want to find them again by key.
In fact, an array (in Java) is nothing else than a collection of variables (all of the same type), which you can index by an int.
(And the scripting languages which allow creating new variables on runtime implement this also with some kind of map String → (anything), where this map is either method/script-local or belonging to some surrounding object.)
You wrote in a comment to the question (better add those things to the question itself, it has an "edit" button):
Without getting into too many details, I'm writing an application that runs within a larger program. Normally, the objects would get garbage-collected after I was done with them, but the larger program maintains them, thus the need for a unique name for each. If I don't give each a unique name, the old object will get overwritten, but it is still needed in the context of the greater program.
So, you want to retain the objects to avoid garbage collection? Use an array (or List or anything else).
The thing is, if you want your larger program to be able to use these objects, you somehow have to give them to this larger program anyway. And then this program would have to retain references to these objects, thereby avoiding garbage collection. So it looks you want to solve a problem which does not exist by means which do not exist :-)