SYMPTOM:
User DSN does not appear in the drop down list of available DSNs for the Translation Table that can be defined with Repository Translation Wizard.
In the ODBC Data Source Administrator, User DSN, "TestUserDSN" can be seen as shown below:

However in the Repository Translation Wizard, this DSN is not listed while all of the other System DSNs are available:

CAUSE:
The Repository Translation Tool is working as designed. Since User DSNs are available only for the user login to the session, there is a high chance that the Service account or some other user account have problems connecting database with User DSN. Therefore, System DSN should be used.
ACTION:
Use System DSN to avoid this issue.