You can name any object by selecting it --> RMB --> Properties --> General , but how can you control the font and character size?
Solution
When you are in Preferences --> Visualization --> Names/Borders tab --> Show Object Names --> Set it to Work View or All Views, then you can see the object names.
Then you can go to Preferences --> Visualization --> Color/Font tab --> Session Settings --> Font to change the font and character size.
Notes and References
Hardware/Software Configuration
Platform: all
OS: n/a
OS Version: n/a
Product: NX
Application: SYSENG
Version: V12.0.2
Function: VISUALIZATION
Ref: 001-6919167