I'm cool with them just not having a proper name, and being given different names by different people in different situations. I'm cool with characters just saying "Alien," to be completely honest. "Snatcher," "X-Ray," and "Demon" all worked just fine for me in the recent novels as names that characters came up with to describe what they were seeing; in Aliens the term "Xenomorph" was nothing more than a catch-all umbrella term for the organism that the marines had not yet encountered, not a definitive species name like the media that followed seemed to make it out to be.
"Xenomorph-XX121" is better because at least that one is putting a descriptor at the end of the general term to give it some sort of actual identifying factor though it is also a bit of a mouthful for characters to be saying to one another.