Names that end in "kichi" (written in kanji, meaning "good fortune") have an "old-fashioned men's name" feel to them. It's a name ending that gives the impression that the person is probably an older guy. And perhaps from a rural area (though I'm less certain of that.)
Some examples of names that real people have had include
* - Daikichi
* - Harukichi
* - Koukichi
* - Masakichi
* - Sakichi
There are far more than that as well.
The creators of Animal Crossing took advantage of the fact that tanuki ends with "ki," so it's very simple to make it Tanukichi and anyone can instantly understand that this is an older male tanuki character.
As an aside, Redd, the fox rival of Tom Nook, is called Tsunekichi in Japanese. The word for fox in Japanese is kitsune.