Rather late, but if you still struggle with this the issue, or for others that find this :
Splunk dbX drops table name and only uses the field name. (the 'shortnames' option mentioned). What you can to do is alias fields with the same name in both tables.
SELECT DISTINCT a.ProcessGovernance1Up AS 1upa, b.ProcessGovernance1up AS 1upb, <other fields you want> FROM [LOG].ActivityDetail a INNER JOIN setup.ProcessGovernance b ON 1upa=1upb WHERE 1upb=3 AND Severity = 3 AND IndentLevel=1;
You may be able to replace <other fields you want> with * but I'm not sure without testing.