I generally just try to create names that sound suitably exotic and have a general phonetic similarity to each other, though not too much. If it's an existing species, I try to come up with names that sound like part of the same linguistic background as known character names. Sometimes I base names on private in-jokes, for instance if I'm basing a character on the mental image of a certain actor, I might start with the name of that actor or one of their characters and mess around with the sounds until I come up with something that nobody but I could possibly recognize the origin of (since, in-universe, there's no reason alien names would actually be based on anything Earthbound, so I avoid making any in-jokes too obvious).
Sometimes, if I need an alien name and I'm drawing a blank, I'll just look around, find some word written somewhere, and anagram it. For instance, I must've written part of The Buried Age while sitting on my couch next to my bicycle, because I took the name of the ancient B'nurlac race from the Blackburn-brand pannier rack on the back of my bike. I get a lot of alien names from anagramming.
For my Hub stories in Analog, I tend to come up with alien names by randomly mashing the keys, then finding some reasonably interesting pattern in the resulting string of letters and tweaking it into a semi-pronounceable name.