Part of me wishes there was more difference between Cove's personalities. I was a bit disappointed while replaying the game many times.
Yeah, it seems like they stuffed what little personality difference he has in the choices; he's essentially the same throughout each stage, and I only fiddled with the personality change they give us in the last two stages, and the only difference were that occasionally he'd do something/respond minorly "with a confidence/outgoing touch" to the text; I forgot the exact words they used, but basically the text said he did it as an "extrovert", or he did it as an "introvert", without really giving us anything solid in his words or actions to express such a personality.
I think the only times I notice a personality change is when MC picks certain choices; for example, I played my MC very dominant/assertive/extroverted, and Cove always gave a submissive/meek/introverted response, but when I switched it up, and started picking submissive/meek/introverted choices, Cove started responding more dominant/assertive/extroverted, regardless of his personality at the time.
I'm also not sure if your disposition to Cove matters too much, but not so much in my case, as I've played with both being shy and direct (can't remember the levels' names

) while picking outgoing/shy choices, and nothing really changed to fit my character's choices; this seems to just cater to the text and people occasionally either being not surprised how bold you are, or sympathetic to your embarrassment outside of choice text. Because I've decided to pick shy/submissive options to experience Cove's assertive/dominant side, I thought it would only make sense to make my character have a shy disposition to her crush/love for him.
It's not a great difference (for replay-ability), but it works for catering his core personality to one I could be comfortable with (I like edgier/extroverted/dominant guys).