JWBI dont know if there is a command to remove the player name but here are some other alternatives:
-using a special hud that doesnt include it (or removing it from your hud)
-disabling your entire hud with cl_drawhud 0. this also removes crosshair unfortunately. if you use lawena there is an option to disable hud elements but not crosshair, but it only works with the default hud so killfeed will be default hud.
lawena's "killfeed only" option is actually just a hud with everything except the killfeed turned off so you could just replace the killfeed files with one from another hud to have whatever killfeed you'd like.