SETLOCAL
SET "_YourPath=C:PathToFiles"
SET "_NewNamePart1=Pirateday ("
SET "_NewNamePart2=)"
FOR /R "%_YourPath%" %A (DSC_*.jpg) DO @(
    FOR /F "Tokens=* Delims=DSC_0" %a IN ("%~nA") DO @(
        IF NOT EXIST "%~dpA%_NewNamePart1%%~a%_NewNamePart2%%~xA" (
            MOVE /Y "%~fA" "%~dpA%_NewNamePart1%%~a%_NewNamePart2%%~xA"
        ) ELSE (
            MOVE /Y "%~fA" "%~dpA%_NewNamePart1%%~a%_NewNamePart2% %Time::=.%%~xA"
        )
    )
)
ENDLOCAL