The TV in particular likely does not have this feature. When cycling through the menu which gives you the generic input names you mentioned earlier, press on the blank one, if there is one, and it should give you a option to enter a custom name. If not, then your TV isn't capable of such a feature.
From my experience, the only TVs to have this feature are a select few Panasonics. None of the Samsung, Sony, or LG TVs I have worked on have had this feature.