On Fri, 30 Sep 2016 04:21:54 -0400, tlvp wrote:

Not here (Android 2.3.5): I long press on an app icon (in the display of
all apps) and an options dialogue comes up: [ Add to Home | Add to group ].

Or, I long press on an app icon on a home screen and when the icon vibrates
I can drag it elsewhere, wherever I want.

But rename it? Sorry, not here

You need a launcher that supports naming.
I realize you are on Andriod 2.x while I'm on 4.x, but one question for
you:

Does your Android support the Nova free launcher?

If it does, Nova free is fantastic and does a *lot* of things the stock
launchers don't do (e.g., mine came with the TouchWiz launcher which sucks
by way of comparison).