Asgore - Asgore was the past king and Toriel's Ex-Husband.
Alphys - Alphys tried to fight Toriel many times before becoming the leader of the royal guard but failed. Toriel offered to train her to fight and then she became the leader of the royal guard.
Undyne - Undyne is the royal scientist and Toriel has offered her to experiment with determination
Toriel's apperance is just like Asgore's in undertale but she has a staff and shorter armor with a shorter cape.
Her personality is much more kind then Asgore in the original UT. She is depicted as being a calm queen, and known to be very kind. She feels deep regret for killing children that she wished she could have raised as her own. She will make an offer of pie before the battle, and follow through if the protagonist agrees. As Queen of the Underground, she is often depicted as being overtly motherly to her subjects, old and young alike, tucking them in bed, reading stories to children, and disiplining any troublesome teenagers.
- Some was copied and pasted onto here from the Underswap wiki, please go check them out for more info