Say you create a hole, then name it "X".
Now do a feature array on the hole - the arrayed holes will have the same name ("X").
If you check that option, the individual holes will have an index added ("X1", "X2" or "X_1", "X_2" or whatever)
Production: NX10.0.3.5 MP16/TC11.2
I'd rather be e-steamed than e-diseaseled
"Lets you add a number to the end of a selected name, beginning with the number you specify in Starting Index."
You can assign the name to features/components (Different than assigned in Part Navigator/Assembly navigator) and they can be displayed in NX UI.
For example, I have created three points and I want to distinguish them from each other to use them. I can select them > RMB > Give some meaningful name, Select the option 'Add index to name' with starting index as 1. Names will appear with each point with given name followed by an index. By default, 'Show Object Names' is turned off you need to enable it.
Menu > Preferences > Visualization > Names/Borders tab > Under Part Settings you can change it by selecting options available
Same is applicable for the components with respect to assembly.
Note that, It will name only geometry not features in the part navigator and components in the assembly navigator.