Awk
solution:
awk 'BEGIN{ FS=OFS="," }{ $0=$0 OFS (++a[$1]) }1' file
The output:
John,Guitar,1John,Vocals,2John,Piano,3Paul,Bass,1Paul,Vocals,2George,Guitar,1George,Vocals,2Ringo,Drums,1
The same with print
operator:
awk 'BEGIN{ FS=OFS="," }{ print $0,(++a[$1]) }' file