Is it considered a joke to mock others by saying "another bearded one"?

The aforementioned statement is not mockery. However, if by your words "I work with the doctor" you meant that you are under his authority, then this is a lie from which you must repent. But if you meant that you both work in the same government department, then there is no harm. And your statement to the doctor "Azhari," if it is true or if you meant that he is like the beloved Azhari, then there is no problem; otherwise, it is a lie.