Re: lumia 625 operator logo
Depends on if you are talking about the operator logo on the case, or on the display when the phone is booting up.
If this is the "display while turning on the phone" logo, you can't. Not without flashing the phone, and that could turn your phone into an unusable brick.
If this is the physical logo on the back cover, then you can either purchase a new cover online, get a case for it to hide the cover, or paint it.
That's about all the options there are.