I wonder why she's freaked out. Calling out someone's name during sex is not actually that unusual, and at least she's not calling out someone else's name, you know? So what's her problem? Obviously she has one, and I'm not sure that telling her to loosen up is going to help.

This is my guess, based on my experience: Sometimes the emotions that one experiences during submission feel a lot like other emotions, even sometimes like love. It doesn't mean that they are love, but it can be confusing.

You mentioned that you "have been playing with this sub for a little while now" so it's not clear what the status of your relationship is. Maybe she just wants to play but finds that her feelings during sex seem different. Maybe these feelings are similar to, but more intense than, ones she felt in an ongoing loving relationship (since she didn't call out the name of her long-term partner), and she is troubled by the fact that in a loving relationship she did not have this intense reaction, but in a play relationship she is.

I would suggest talking with her about how D/s can elicit strong feelings and reactions and make it clear that she is calling out your name because you are her Dom. Give her permission to feel strongly but give her room to figure out that what she is feeling might be something new, not something she's experienced before. This is something that she can figure out for herself; you don't need to tell her.

I would strongly suggest having this discussion as her Dom and not as her boyfriend or lover. These are tricky waters - you want to help her with her feelings but whether you are going to have the Relationship Talk should not be based on this situation.