L.
Yes, this is very normal. I have a daughter who, at 3, introduced herself at Sunday School with the middle name of "Cinderella" and then proceeded to tell that she had 2 brothers, naming one and "the other is the Fairy Godmother"!!!
My "Fairy Godmother" son is now 3-1/2 and he is doing the same thing. He has been everything from "Winnie-the-Pooh" to "Robot" to "Pumpkin" to "Daddy...I'm daddy, mommy. Mommy...I'M DADDY!!!" Much of the time he won't even answer us unless we address him by his name du jour. Most recently it has been Rabbit. Just a (funny) phase they grow out of. You might want to keep a record of some of these funny things they say and do, so you can have a good hearty laugh in a few years...
Oh, and my daughter (now 5) has always called her dolls by whatever they wear or specific "purpose" (green baby, blue baby, white baby, bath baby). Now, she names them, but the names change frequently, usually depending on who her "best" friend is at the moment...