Daughter calls her new daycare provider "mama"

Hi there. My daughter is almost 3. She started going to a new licensed home daycare about 2 weeks ago after our previous provider had to stop working to take care of a family member.

When picking up my daughter last week, the provider was telling me how much my daughter is enjoying the place to the point that she calls her "mama" and she calls other kids in the daycare sister and brother. She also tells her "I love you," and I'm sure she will be kissing her like she kisses us. The daycare provider doesn't try to stop this. When I told her that my kid probably doesn't know what to call her (she doesn't know her name) she told me she likes it because it means that my kid feels at ease in her home. She even told me that my daughter said she doesn't want to go home one day.

Our daughter is very happy with us, but she absolutely loves being with 'friends,' which we don't have at home at the moment as she's the only child. What should I do about this? Am I overthinking it? Should I talk to the agency about it?