Gaster Sans is a fusion of W.D. Gaster and Sans. It happened by mistake. Gaster was glitchy when Sans tried to teleport away from Undyne before she could hurt Sean. Thus waking up in a different location but as one being.
They like to be called they even though they are male, they feel like two people in one body cause well they sorta are.
They still love Sean and see him as a son/nephew.
Due to them being a fusion their personality is also a fusion of Sans and Gaster. This means not much has changed about them and they seem to be doubly strong in battle. It is also hinted at that they could unfuse and fuse back if they wanted to they just chose to remain in this form for now.
It is hinted at the Undyne will be facing them in a battle, if this were to happen the outcome of said battle would either be a win for Gaster Sans or a tie if they choose not to give it their all.
It can be assumed that this fusion can use the same attacks as its two halves like blasters blue attacks. It is assumed that Gaster even has a special green attack that can heal their wounds. But Gaster hasn't been seen doing so.
As Stated they treat him like a son/nephew. They enjoy being with him and talking with him. They make puns with him and draw when they have a chance to sit down and just enjoy each others company.
They don't really get along with Toriel very well for she seems to not trust them and seems to be unaware that they are Gaster and Sans in a fusion.
They bow and show respect to the king but behind his back, they make funny goat based puns and even pull pranks on him.
She sees them as a traitor for protecting a human and sees them as a battle rival. If she does in fact lose to them (which isn't canon yet.) She will keep on tracking them down and wanting to battle them to get stronger. This seems to be boring for them and they tend to walk away and try not to use their full power but she still either ties or loses.