I'm testing upgrading from 3 to 4.  
Is there a way to keep both the usernames and display names in the upgrade?
The username in my version 3 forum were based on a customer number which they use to login but I don't want to loose their real names on a port.  I also don't want to display a users customer numbers to the rest of the users.

Nope, not possible. I think an easy way would be to create a profile field (viewed only by the member and staff) in your 3.4 board and feed it with the customer number. Then you wouldn’t lose it when upgrading. 

You probably would require a help to feed the profile field table. You can try to find someone that still works with 3.4 here: https://invisioncommunity.com/third-party/providers/