These are the characters' nicknames that me and FlamingosDulingos came up with.

Frisk: Starfruit
Chara: Grapefruit(Grape)
Flowey: Mangy
Toriel: Plum
Sans(?): Lemon
Sans(?): Lime
Papyrus: Papaya(Pap)
Undyne: Dragonfruit(Dragon)
Alphys: Banana
Asgore: Durian
Asriel: Mango
☝✌💧❄☜☼: BDA

(At least one of these names will be eventually changed sooner or later.)