Did you know that you can specify a "Custom" Group name? A typical situation is that you'll be grouping on a "system" field, like GoldMine's RECID, which looks like this;
This is usually done when you need to Group by unique values, and grouping on (for example) Company Name won't work as there could be several "ACME"'s in your database. But you'll want something that readable on your report, instead of the RECID.
You can customize what's displayed as the Group Name by;
1. Select Report | Change Group Expert from the top level menu
2. Select the Group you wish to modify, click Options
3. Check the box labeled "Customize Group Name Field"
4. You can either "Choose from existing field" or "Use a formula as Group Name"
Note that after this is done; your Group Name field is now how you want it, yet the Group itself is still broken on the original unique value.