Perhaps serpent. Serpents were long large snakes that could swim and slither on land. So that's probably one.
The scientific name for a Pegasus is "Equus pegasus."
The Minotaur!
As the name implies, it is a snake.
Nurikabe I'm not sure if the spelling is correct though...
There is a mythical creature that was often referred to as the Snake of the Nile. This mythical creature, as stated in his name, was said to be a snake that lived in the Nile River, that was capable of devouring a crocodile by allowing the corcodile to eat it, and eating the crocodile's insides out, therefore killing them.
There is nothing "conventional" about this creature, even for mythological beasts. It does not show up on any search of mythology or cryptid data bases. If you invented it, it is up to you to name it.
the Loc Ness Monster
The Hippocampus is the genus name for seahorses. It is also the name of a mythological creature with the upper half of a horse and the lower half of a fish or dolphin. The hippocampus region of the brain was named due to its resemblance to a sea-horse.
The monster or mythological creature who's name rhymes with wire is a vampire. A vampire is an undead humanoid that feeds on blood.
Spider Turtle Snail/Slug Snake
Well the Hydra is a dragon is some versions and a serpentine creature... I don't know if he counts as a snake though.
The name, Calista, comes from a Greek origin. Calista was a mythological creature that turned into a female bear and now stands for the constellation. This constellation is called the great bear constellation.