When a card refers to itself by name, it really means ‘this object.’ For example, Darkthicket Wolf‘s ability gives +2/+2 to itself. There are some situations where this distinction matters. For example, if Sakashima the Impostor were to copy this Darkthicket Wolf, the ability on Sakashima would effectively read ‘2G: ~This~ gets +2/+2 until the the end of turn.’ It does not matter that Sakashima has a different name.
Mirror-Mad Phantasm also refers to itself by name in its ability. However, it also specifically refers to a card named Mirror-Mad Phantasm. The first instance of its name in its ability should be read to mean the source of the ability (i.e., ‘this object’). However, the second instance should not. This is because the ability refers to a card with a specific name, and is not implying that it necessarily means itself.
For example, let’s assume that a Mirror-Mad Phantasm is copied by a Clone. This Clone will have the Mirror-Mad Phantasm ability, and will be able to shuffle itself into its owners library. However, when this ability continues to resolve, it will look for cards that are specifically named ‘Mirror-Mad Phantasm.’ Once the Clone left play, the copy effect that was applied to it ended, to this object will not have that name. Unless there is another copy of Mirror-Mad Phantasm in this player’s library, this ability will end up putting all cards in his or her library into the graveyard.