Does anyone know why Amanda calls her doll Anabelle in the final scene? The doll is called Mirabelle during the search. Is it because the Mirabelle doll fell into the lake and Amanda got a new doll called Anabelle, or maybe it was actually to show her careless mother didn't even know the correct name of her doll by calling her Mirabelle instead of Anabelle?
Like other's said, and as the last part of your sentence suggested, it's to show that the doll's actual name is Annabelle, not Mirabelle, but her mother pays so little attention to Amanda that she didn't even know the name of her daughter's doll.
It also gives the idea that Patrick, at that point, may be realizing that he, indeed, made a mistake.
What kind of mother doesn't know the name of their daughter's favorite doll?
No doubt. A LOT of babysitting, as Helene surely isn't going to change.
It wouldn't be at all surprising to find out that Patrick had been in some type of bad situation when he were young that gave him the desire to do the sort of work he does.
Those are interesting ideas, but the scene was meant to suggest one thing, and that is that the mother is not the mother she purports to be, and that her daughter is actually not very important to her.