How do I display the function name of an object in a schematic?

You can use translatable or user attributes. Double click on the symbol:

 

Depending on the symbol, the ‘User data 1’ attribute is inserted by default:

 

If the used attribute is not in the symbol, you have to add it. Do the following:

-Right click on the symbol, select ‘Symbol’ option, then ‘Open symbol’:

-Go to ‘Edit symbol’ menu and use the ‘Insert attribute’ option. You will have a dialogue where you can select symbol attributes to insert. In this case we are going to insert the description attribute, but you could select user data attributes too if they were not inserted:

 

-Insert the attribute, close and save the symbol. Then you have to update the symbol in the drawing, do right click over the symbol and select ‘Symbol’ option, then ‘Update’: