The name "Eve" refers to different things on Natural Instincts.
Eve - Mother of All and Creator of All Vampires[]
Eve, as people know her on Supernatural - is known as the "Mother of all" and creator of all monsters/supernatural beings, including vampires. She is older than angels and demons. Although she has been banished to purgatory, her spirit can be called upon in various ways if she allows it - especially in the creation of new species (such as the Daevas) - through magic or drinking her blood.
Eve, as stated, is also the creator of all vampires - and this fact is recorded extensively in the Vampire Bible, a text said to predate the Christian Bible. For those who watch True Blood, she is named Lilith on the show.
Note - she can shapeshift as any appearance she'd like and has telepathic powers with all of her creations.
Eve - The War Child[]
Eve is also the name of the child said to either destroy or save vampire kind in an ancient prophecy recorded by the Solemus species (Being Human). She is made from two Elm Werewolves and lives in a house with a vampire, a werewolf, and a ghost. Read more about the prophecy here