Learn Russian: Её имя опять вылетело у меня из головы.

The verb вылететь literally means "to fly out" (the prefix вы- means "out" and лететь means "to fly"). Metaphorically, it is the standard Russian way to say that something "slipped one's mind" or was suddenly forgotten.

Why does the sentence use у меня instead of a possessive like моей (my)?

While English says "out of my head", Russian rarely uses possessive pronouns with body parts or mental states. Instead, it uses the у + genitive construction (у меня) to indicate who is experiencing the action. Literally, it translates closer to "the name flew out of the head on me."

Why does вылетело end in -о, since the subject имя ends in -я?

The verb is in the past tense, so it must agree with the gender of the subject. Имя is one of the ten special Russian nouns ending in -мя. Despite ending in a letter usually associated with feminine nouns, these are all neuter, so the verb takes the neuter ending -о.

Doesn't the word опять (again) usually trigger the imperfective aspect? Why is вылетело perfective?

Опять can be used with both aspects. Here, вылетело is perfective because the speaker is focused on the sudden, completed result: right at this moment, the name is gone. You would only use the imperfective вылетало to describe a continuous background habit, such as "Her name kept slipping my mind all evening."