The reason of Bartholomeo Kuma's devil fruit named as Nikyu-Nikyu no Mi?
Paw-Paw fruit grants the user the ability to repel everything they touch, and is physically represented as paws on the user's palms, making the user a Paw Human. 
The Paw has variety of uses that leaves a paw-pad imprint resembling the pads on his palms. 


Cats uses one paw to repel inferior life forms. The Paw Of Do-Not-Want. Which might also be the reason behind a paw that can "repel" of your question. Video: https://twitter.com/boingboing/status/596558460382220288
The fruit's name, Nikyu, comes from the word "Nikukyū" (肉球?) which means "Paw" in Japanese.  Ref: Nikyu Nikyu no Mi
I did a little search online if there is a significant reason why its called Nikyu-Nikyu no Mi/Paw-Paw Fruit but I found none that its related to myths or something. So the name "Paw-Paw" is basically just from its Japanese name counter part "Nikyu-Nikyu".