I think this is normal behaviour.
When the switch is first added to Netsight it will use the switches sysName to populate both the System Name and Nickname in Netsight.
Thereafter, if you want to change the displayed name you need to go to the Device>Configure Device->Device Annotation and change the Nickname manually.
If you delete the switch altogether and then add it back in, it will get added with the new name as intended. Rediscover doesn't change the nickname, but the System Name in NetSight is automatically updated without doing anything.
As the system name will always automatically update in Netsight to any change on the switch, there might be a way to have it update the Nickname to match, you would perhaps expect as DH says a rediscover to do this - so that would be interesting / useful to know or be added as a feature request?