You pose an interesting question, so I'll provide equally interesting questions to better enable you to craft your character ..
One, what kind of people are your "mermen"? Atlantis was in fact a Greek myth/name and so any character name associated with Atlantis invariably has a greco-roman sound to it (and the population has a similar look).
Are your fictious people strictly water-breathers or amphibious? That seems silly until you realize that certain sounds don't transmit as well under water -- if you don't believe me, put your head in a sink full of water and say your name, your friend's name, your dog's name, and see what I mean. I think water-breathers would have vowelish names with lots of long "e" and "i" sounds -- think of whale calls.
What is the point to naming your character at all? If she's a main character, all well and good, but if she's a fringe character that the mc interacts with, why bother with a name? Names are HUMAN traits, it's how we with our limited senses and abilities make sense of the world. Humans are very visual, so we describe things we see and name them so we can tell them apart from other like things. I don't think dogs-people (canine-type humanoids, rather) would name things as they simply are what they are -- each individual different by smell, for example.
I know this doesn't answer your question, but hopefully this will help you analyze your character, and see her for more than just another "Ariel" (A character from a Shakespearean play before she was a mermaid by the way)