Does it make sense to apply the quality of "Identicality" to one or multiple objects?

I'm writing a script which involves the comparison of two objects. I keep finding myself referring to this sort of test as an "identicality" check. From my preliminary research, "identicality" does not seem to qualify as a word. Also, the more I think about it, the less sense it makes to me. A single object should not be able to posses the quality of "identicality", since it requires that a second object exists for comparison, yet makes no reference to said object.

Does it make any sense to refer to the "identicality" of two objects? Should it instead be "identicalness", if that makes any more sense?

I'm not sure if "identicality", or even "identicalness" is etymologically sound either, or if it is just my mind kludging things together.

Solution 1:

It makes sense to refer to the "identity" of two or more objects.

Of course, outside maths, this sense is usually obscured by the 'distinguishing character or personality of an individual : individuality' [Merriam-Webster] sense.

I had to search quite a way on the internet for:

A human gene that shows identity with the gene encoding the angiotensin receptor is located on chromosome 11 ...

As Peter Shor points out, choosing the lesser of two evils makes sense (if one can sort out which it is). ODO lists

identicality N = identicalness.

Origin Late 19th century.

It makes more sense to use this unambiguous word (it must refer to multiple objects) until it becomes more common than the 6th-most-common sense of 'identity' Webster's lists. And to continue to do so.

Solution 2:

Identicalness is a word and I think it's the right word for your situation.

Identity could be used too, but is liable to be confusing due to its more common meaning of "being the same thing" as opposed to "being alike in every way".