[...] do you know if there's a way to get a display name that can be used in menus and stuff from item definition indexes?
tl;dr: For menus in particular, not easily.
I'm not sure what you're referring to when it comes to GetEntityClassname, but there's two options for item names:
TF2Econ_GetItemName returns the non-localized item name. It's limited to English-only, and the non-localized item name may not match the English-localized one (it still refers to "The Huo Long Heatmaker" internally instead of "Huo-Long Heater", among other ones).