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
I have an internal mindscape. It’s closer to a layered interactive data stream than anything else.
One of the ‘nodes’ on that is my speech center. Unless I block it, it tries to turn the data stream into a word stream. They then loops into the auditory ‘node’. That then tries to process it the same as someone else talking to me. It lets me use all the filters and processing tools I built up as a child. It is excellent at finding holes in my ideas, the same way I would mentally pull apart what I was being told by someone else. It also lets me crystallise ideas into a form that can be passed to someone else.
I can suppress my inner monologue (unless I actively require it, e.g. for writing this message) but generally I don’t. It’s useful when I need to deep dive a problem. My brain can outrun my word stream, and dropping it can let me attack problems without the limitations of language caging me.