Dumbo's name in this movie comes from a sign that originally spells "Dear Baby Jumbo". After the D falls down and knocks off the J, the sign suddenly spells "ear Baby Dumbo" - and although the audience only cares about the "Dumbo" part, the "ear baby" part is very fitting due to Dumbo being a baby with big ears.
The original Dumbo film ended with Dumbo discovering his ability to fly and becoming the circus's star attraction. This film is a tale that focuses on what happens after Dumbo achieved success.
Dumbo and his mother return to the jungle in India. In Disney's 2016 Jungle Book adaptation, the elephants were described as being gods, so Dumbo's flight ability couldn't be a coincidence.