No they do end their prayers like that. You can hear it both ways. Except its 'In the name of' not 'to the name of'. Anyway, the Holy Ghost is just some kind of spiritual "other" that is watching you at all times. Gods CIA spook. It's undefined in mormon theology, like a lot of other stuff.
The only mormon prayer I recall using this form is the baptismal "prayer" and possibly some ritual in the temples.
In Mormonism, the Holy Ghost is the "messenger" of the godhead, kind of like Hermes or Mercury in a way. Since the father and the son are physical entities, the holy ghost is how god haunts you, essentially, how he "whispers in your ear" without annihilating you with a glorified physical presence.