"So when they had gathered together, they began to ask him (αὐτὸν)...."
αὐτὸν is from the personal pronoun αὐτός.
This pronoun can take either masculine endings (which match those of λόγος, a masculine noun you know) as in he/him/himself or feminine endings (which will match those of ἀγάπη, a feminine noun you have seen before) as in she/her/herself.
It can also take neuter endings when referring to a neuter noun...but we are not going to deal with neuter endings yet.
Try to identify these forms of he/him/himself // they/them/themselves. If you don't know the answer, go ahead and click on your best guess.
What sort of word is αὐτοῦ?
What sort of word is αὐτόν?
What sort of word is αὐτῶν?
What sort of word is αὐτοί?
What sort of word is αὐτῷ?
What sort of word is αὐτούς?
What sort of word is αὐτός?
What sort of word is αὐτοῖς?