It is possible with GNU sed. Choose one of these two forms based on the greediness of the replacement.
sed 's|=.*,|\L&|' file
sed 's|=[^,]*,|\L&|' file
As the manual states, "`\L` turns the replacement to lowercase until a `\U` or `\E` is found". `&` is the text matched by the regex.
* * *
I have modified the sample file to show that you should wisely choose between the geedy `=.*,` and the non-greedy `=[^,]*,` regexes:
$ cat file
SOMENAME=WOODSTOCK,
SOMEOTHERNAME2=JIMMY,WOODSTOCK,FINISH
$ sed 's|=.*,|\L&|' file
SOMENAME=woodstock,
SOMEOTHERNAME2=jimmy,woodstock,FINISH
$ sed 's|=[^,]*,|\L&|' file
SOMENAME=woodstock,
SOMEOTHERNAME2=jimmy,WOODSTOCK,FINISH