Is "Gomer" a typical southern name

Well... I went onto ancestry.com and entered just "Gomer". Got over 10 million hits!

Is it common? Looks like it once was, from roughly 1800-1940 peaking in the late 19th/early 20th century and then it very quickly fell out of fashion, even before the show began. I've broken it down by 20 year blocks. One thing I noted was that the name Gomer in the 1960 block was typically in quotes, suggesting that it recent use is as nickname - probably given because of the show.

1980-1999: 862
1960-1979: 8022
1940-1959: 67205
1920-1939: 504094
1900-1919: 2020796
1880-1899: 2771262
1860-1879: 2145403
1840-1859: 1273726
1820-1839: 879627
1800-1819: 565408
1780-1799: 236480
1760-1779: 92419
1740-1759: 45796

Is it southern? No.

You'll find it in the south, yes, but not disproportionately so. I just picked out some English speaking countries and some states at random. The numbers by these states are pretty big. I suppose you could argue that, yes, Pennsylvania had a bigger population than Kentucky, but the fact remains: if you lived in the US in 1900, you probably would run into someone named Gomer sooner or later. Today? Not so much.

United States: 8014979
England: 841957
Scotland: 97531
Wales: 74483
Ireland: 25006

NC: 470171
VA: 556706
KY: 587165

PA: 781768
NY: 577040
IL: 572388
CA: 356573

I believe about 25% of men in the south are named Gomer. 25% are Goober, 25% are Jethro, and the other 25% are Jed and Jeb.
This is according to the census bureau!