No, literally "rich root/origin/character". Closest you can get to "fennec" [fu(e)nekku] while still sounding like an actual Japanese surname.
...Okay~Fune~
Let me look at your homework, please!Oh... Okay~Fune~
Let's hold hands!Okay~Fune~
I forgot my lunch box, please feed me~!Huh!?
Well, fine~Fune~
I forgot my umbrella, so let's go together~!snap