A cover song is your own version of a song that you did not write/compose.
Whenever you record a song that someone else wrote, you need to get permission from the copyright holders.
In order to obtain a mechanical license you may use cover songs licensing service like Songfile
Using original artist names
A mechanical license does not permit you to use the original artist name who performed the cover song.
If you are releasing a cover of led zeppelin you may not use "led zeppelin" in your metadata - this name is protected by a trademark and using this name would require an additional license or permission from those controlling the rights to this trademark.