Did you ever try looking for them in other census records as I suggested? Also, try looking for death certificates for other members of the family in the household; as I said before, don't limit yourself to just the names of your ancestor, research the rest of the family and anyone else in the h/h, and be sure to check out the neighbors, quite often, they were related.
As for the names of the children, that's not unusual, many times they didn't keep the same names as when they were young, most children weren't even given a name before 1 -2 years old. And of course, there's always the chance of middle names, they may have alternately used first & middle names in some records. But you have to do your census work, otherwise you're wasting your time.
Here is what I said in the Census that I found your family in:
1930 Morgan County, Georgia, City District, District 2, Image 10, #117/119:
JIM EVANS - NEG - 50 - M - 20 - GA GA GA - FARMER (1st married at age 20)
ROBERTA EVANS (wife)-NEG - 44 -M - 18- GA GA GA (1st married at age 18)
GILBURRON EVANS (son) -NEG -17 -S - GA GA GA
CLAUDE EVANS (son) - NEG - 15 -S - GA GA GA
CLYDE EVANS (son) - NEG - 12 -S - GA GA GA
ALBERTA EVANS (dau)-NEG - 2 -S - GA GA GA
Aside from the names of the family in the household at the time, this census
tells me a few other very important things;
1) James/Jim Evans(b. 1880) was first married at age 20, that would be abt
1900. Roberta (b.1886) was first married at age 18, that would be abt
1904; obviously, this was at least a 2nd marriage for both of these
2) There is a wide spread in ages between the 2 youngest children,
obviously, it is likely the youngest is a child with Roberta.
3) The entire family was born in Georgia.
It is likely judging by the name on Claude's death certificate, that his
mother, Mattie Griggs, died at least after 1918 (the age of Clyde Evans),
but before about 1927 (Alberta was born in 1928, deduct at least another
year for James & Roberta to have married and that brings you to abt. 1927).
I don't see this family in 1920, and think that you will have to do some
really good census work to find JAMES/JIM EVANS in GA in the census from abt
1880 - 1910, but at least now you know the age to look for.