It's quite common for the mc self insert to be called 主人公(protagonist) in these types of situations, despite the main moving force being the girl instead. I think it makes sense if you're willing to self insert, but some readers might only take a third person view of it, so it's a bit awkward if it's like that.
If you've listened to any Japanese ASMR you'd know that the girls always refer to you by skirting around the fact that you're a nameless self insert through pronouns, titles, or just adding -kun to whoever you are in relation to them, such as (幼馴染くん)childhood friend-kun