Example 2 in the article linked below provides a means to automatically add the Active Directory domain to a user’s username when they attempt to login using the ADFS login form.
Warning: FrontEdge is not responsible for any negative side effects that result from implementing or mis-implementing the suggestions/instructions in the linked article. Take a backup of any files that will be edited as part of this process prior to making the changes. Rigorously document the changes being applied. Please also note that future patches and services packs to ADFS may require these changes to be reapplied and/or break these changes.
Article: https://docs.microsoft.com/en-us/windows-server/identity/ad-fs/operations/ad-fs-user-sign-in-customization under "Advanced Customization."
Then follow the instructions here:
Example 2 provides the means to automatically add the domain when missing.