Furthermore I decided to find out what the names mean and compare those findings to the characters and the plot.
Due to those homepages
The name "Reeve" seems to come from the name "Steward", which is connected to the word "bailiff", which is the appellation of an officer with authority in jurisdiction in the Anglo-Norman language.
As far as I read the story I can not claim that this is Reeve's mission in the story, but maybe he will be part in the clarification of the past events.
The name "Jane" is of course very common in the English-speaking world. It is Hebrew and means "good is gracious".
Without knowing how the story ends it is already clear that Janie is a gift for her grateful parents. The question is, whether she was originally given to another family. Finally she is a gift for Reeve.
The name "Elizabeth" means "my god is a vow" and I can not figure out how this name matches the story, but as it is common to have second names maybe it was just added, furthermore it does not play a big role in the story and was called just once yet.
The meaning of the "other name" (the girl on the milk carton) is white, fair and smooth, which probably fits to Janie as people with red hair usually have a very fair skin.
It is interesting that both names "Janie" and "Jenny" are phonetically so close to each other.
Janie tries to match herself to her parents. In this context she thinks about several differences: she is the only one with red hair (Cooney 1990, 18) she grew later and is smaller than her classmates (ibid. , 8).
Even regarding features that do not at all proof, whether she is their child: her parents like to talk, whereas she does not (ibid. , 34) different looking feet [Janie is still growing!] (ibid. , 33) they do not laugh in the same way (ibid. , 18)
And to come to an end:
I do not own this foto! : http://whatscookingamerica.net/PegW/DogwoodCake/DogwoodCake.htm