Inventor added a nice feature a few releases ago that you may not be aware of: File Naming Defaults.  This (2) button is stored away in your Application Options at the bottom of the (1) File tab.

If you open this dialog box, you will see that you have a set of tabs to set up the default naming scheme for Frame Generator parts and assemblies (added in Inventor 2019.2), Tube & Pipe parts and assemblies (added in Inventor 2020), as well as mirror and copy filenames (added in Inventor 2021).

This allows you to predefine the filename for files that were automatically generated in the past.  For Frame Generator components, you can select from a (1) list of options to build a filename, such as (2, 3) Stock Number and (4, 5) Index Number to give you, for example, C 3 x 3-001.ipt

You can do this for the Assembly, the Skeleton Part, and End Caps, as well as the Frame Member as shown above.  Pay close attention to the other options in the dialog box, such as the locations (paths), whether to use assembly units instead of part units.  It is quite a nice feature to be able to use and you can still use the Unique numbers that you have been used to seeing, but if you opt for Index Numbering, you can limit the number of characters to suit your requirements.

Under the Mirror and Copy tab, you can opt to keep the _MIR and _CPY filename for all mirrored and copied parts or you can use your own permanent suffix and path that you create with the optional attributes, such as a Date, Project Name or Unique Number.

File Naming Defaults is definitely a dialog box you will want to explore and test out scenarios in order to make filenaming more legitimate and functional for your parts and assemblies.