For me there’s two separate participants, a ‘talker’ and a ‘listener’. My mind identifies more with the talker, because that’s the one that has agency. Since there are two participants, both of which are me, I talk in 1st person plural (‘we’ve got to do …’, 'we thought about this earlier’). I stopped being afraid of being alone after I started having an internal dialogue around the age of 11, since having a second participant in the conversation meant I was always in company.
Edit: Wow, looks like there’s a lot more diversity in this than I was expecting
If it’s not music lyrics/no lyrics music, some other thing I have on my mind that isn’t something I came up with, a remix of something I have seen, or a memory and/or dream, I usually end up having fantasy conversations where it’s me but using someone else’s voice. Specifically because I don’t currently like my voice and think I sound like a gremlin.