"Mama Mer-Pup" is not an official name yet. It may have been referenced in the storyline as such, but has not been officially named. Alternatively, it may be a name popular among fans, but has no official basis.
Not much is known about Mama Mer-pup, but we have learned some things. For one thing, neither Mama Mer-pup nor her baby seem to be able to speak, but instead make typical dog sounds, like whining and barking, a clear indication that they have not acquired a language yet. They do, however, have the strange ability to turn other pups into mer-pups simply by touching that pup's nose. The pup will remain a mer-pup until sunrise. This only seems to be possible under the Mer-Pup Moon.
Mama Mer-pup seems to have a worrisome personality to her because she seems to panic whenever her baby is in danger. But she will still do all she can for her pup before going to get help. Because she can't speak any language other than dog-speak, it is very unlikely that anyone will understand her by those standards.
Both Mama Mer-pup and her baby resemble Skye's appearance except they have dark grey and white fur instead of the more golden colors of Skye's fur. They have sideways fish tails that are yellow with a jagged purple stripe around the middle and purple markings on their tail fins. They also wear black collars with gold pup tags for some odd reason. She also somewhat resembles Chase, Marshall, and Zuma.