Where do the Angels get their names from?
Seele has knowledge of when the Angels will appear based on the Dead Sea Scrolls. (That they have knowledge of the order of Angels from the Scrolls is indicated in an ep. 23 conversation. In an earlier episode, there is also an indication that Seele is expecting an Angel to appear at a certain time; I do not have access to the anime right now and cannot find the exact reference.) With this in mind, it is not surprising that the Dead Sea Scrolls also probably contain the names of the Angels.

It is unlikely that Seele was only provided with knowledge of the order of Angels and not their names. Note that Kaworu speaks of the descendants of Lilith in one of his conversations with Shinji. Lilith is the name of one of the first Angels, and as  Kaworu is an Angel, his usage of the name indicates that it probably is not just a name that Seele assigned, but rather, a real one.