Tell me what does TSR mean? And also please tell me how to add TSR on logo?
I think you mean TRS. (Top Rated Seller)
Check this out: https://www.fiverr.com/levels for helpful information.
Scroll to the bottom for TRS.
That is not logo . That is badge or level . When you will be Top Rated Seller (TRS) you will get the TRS badge attached with your profile pic. And you can checkout the given link by @lloydsolutions to know more about the level system .
It is not allowed to add a seller badge on any of your picture (profile or specific gig picture). Doing this is being considered a serious vilolation of fiverr’s TOS.