I don't think so, oracle will get confused with the same global name (i.e mydb.abc.com) in a network. But if it's different domain then there's no harm to create it. Like "mydb.abc.com" and "mydb.xyz.com".
I have Personal Experience running the the 2 database with the same SID on the Same Network.
I have Developer 6i, and Oracle 9i.
Connect String will automatically Decide into which database Form will be Login.