We have the desexing tag, which someone set-up a while back as the go-to tag for this sort of thing.
Unfortunately, while it is the correct term, "desexing" is not the word the average person uses when referring to this process.
Over my time editing questions, I encountered questions tagged using variants of spay / neuter / fixing, which are all covered by "desexing". They were all re-tagged with that term. This has the unfortunate side-effect of eliminating the possibility of non-moderators being capable of creating synonyms.
Due to the frequency of re-tagging, there will not be a build-up of incorrect tags for quite a while.
I suggest the following synonym list be created and applied via moderation, and poll the community for any additional:
- fixing -> desexing
- spaying -> desexing
- neutering -> desexing