The default joint name created is simply the joint type followed by a disambiguating number. Clearly this can be changed as you go, but this step could be avoided in many cases if the default was 'name of first component to name of second component' followed as before by a number to disambiguate. The joint type is already indicated by the icon, so repeating it in the name isn't strictly necessary. For backwards compatibility, this mode could be enabled or disabled as a configuration option.
Names such as "Axel to Bearing 1", "RetainingPin to Shaft 1", "LockCollar to Shaft 2" become much more useful right out of the gate.