Well, this goes along the line of someone with tulpas, or basically sentient personalities that are all individual. The text might come across as third-person if written in this way.
I've spent some time with people with said personalities, and their way of differentiating each personality is by saying each line of text differently, sometimes with a different pronoun (as not all personalities have to be the same gender.)
Besides making each name be at the beginning of the dialogue, depending on how the story is written, and whether the person is communicating by text or actually speaking can all effect how clear it is to the reader, because the tone could vary. In general, it might be best to avoid making personality changes too often, unless you are intentionally trying to disorient the reader. But, let me show a little bit of a demonstration.
Examples:
Avoiding Gender Pronouns:
* <PERSON> was cold, but so was <PERSON>, the temperature letting there be no peace no rest between the two in <PERSON>'s mind.
* <PERSON> could never find the right shoes, but another silent opinion said otherwise.
Using Gender Pronouns:
* <PERSON> loved the smell of fresh-baked cookies in his house, but she also thought it never smelled fresh. 873
It seemed like nothing was perfect for her, even if it was for himself.
* <PERSON> took a good look at himself in the mirror, but who was he really? One one hand, there was <PERSON>, and she was nice at least. On another hand, there was <PERSON>, and hearing that voice tell him how awful he looks today just makes <PERSON> want to snap.
In Dialogue, Including Another Character:
* <PERSON> looks to his friend in front of him and asks politely, "Why is it you seem so down today?" There is a small silence between the two. "Oh, it's just about what happened last night." This time, <PERSON> decides to reply openly, "Well, you need to get over it already."
* His friend was lingering on the response from <PERSON>, thinking how rude this is. "Why did you have to say it that way?" However, this time, <PERSON> comes to the front of <PERSON>'s tongue, speaking in a different tone. "Oh, I didn't mean that at all."
Experiment with yourself a little, see which way you like the most.
I hope by some means this was a helpful insight, I wish you luck with your writing! 627