Keeping the Statstring is pretty important. If configured correctly, it lets you know what each soldier is and isn't good at at a glance, while in combat.
I'd suggest, if the GUI has room enough, to present both the proper name and callsign on the soldier stats screen, both in base and in battlescape.
There should be an option for Callsign + Statstring [As opposed to Name + Statstring] in the Battlescape overview screen [Where space is very limited]