My SO has a 4 year old son— as do I. My son calls him daddy (his real dad has never wanted him)

My SO’s son’s mother has him 50% of the time so she’s in his life as much as my SO is.

Last night his son called me mama and kept saying it over and over. He also said he wants me to pick him up from school— and I’ve noticed he’s grown closer to me. (We have been together for awhile- no worries)

Anyway, my SO keeps correcting him because him and I agreed that there’s no need for him to call me that especially since I find t disrespectful to his mom if I allow that...... /: lol. Not saying he’s disrespectful he’s only 4.

But anyway.. what would you do in this situation?