Linux find command and copy and rename them same time

You can do:

find /src -type f -name '*.log' -size +2G -exec cp {} /dest/{}-$(date -I) \;

Additions/Modifications i made:

-name '*.log' searches only for log files, as we are only interested in those. You can look for files with any names too if unsure, just omit -name '*.log in that case
$(date -I) is command substitution the output will be today's date in format YYYY-mm-dd, you can also define a custom format, check man date
End the -exec action of find with \;

CodeHunter