create one private database link for two users oracle
When you select from a table with dblink first time in current session, then oracle needs to connect from one server to another.

So your current oracle instance is SRV1, and other is MYDB. When you issue first time in current session

select * from t@mylink


then oracle create session from SRV1 instance to MYDB instance. How oracle do it? Sends the connect command with username, password and TNS name (MYDB here). This information we provide when create dblink - user, password, TNS name (db name). 

You need TWO private database links, first for one user (A), and the second for another (B).

SQL&gt; connect a/password@SRV1
SQL&gt; create database link mylink connect to user_from_MYDB identified by some_password...

SQL&gt; connect b/password@SRV1
SQL&gt; create database link mylink connect to user_from_MYDB identified by some_password...