Hi,
If it is staying during a session (which might be "all day") but not after you close the app then it will be because you have lost the Read and Write Permissions to the place where that info is kept.
The "Card" you are showing is the one using the Buddies Menu after highlighting Buddy in a List.
The First Name, Last Name and Nickname write to the Contacts App.
Do this to check the Contacts app.
Open the Contacts App and go to Preferences.
In the Preferences Select Template.
Use the Add Field button to Add the Nickname field.
Then choose a card of one of your Buddies and Add a Nickname via the Contacts App > Edit button.
After closing the Contacts App does this Nickname appear on the Card when using the Buddies menu (like your Pic) ?
Does it "Stay" after closing down the Computer and restarting ?
Check it the other way as well.
Does it "Stick" if you add it in Messages via the "Card" you see in the Pic you posted ?
This should tell us if it is the Contacts App that stores this or whether Messages does.
9:01 pm Friday; February 13, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad