Yes while its running, locking has no bearing as a FD uses a link not a name while its open.
FOR %%G IN (*.log) DO ren "%%G" "%datename%_%%G"
nginx -s reopen
sleep 5
move /y %datename%_*.* data
FOR %%G IN (*.log) DO ren "%%G" "%datename%_%%G"
nginx -s reopen
sleep 5
move /y %datename%_*.* data