How to reference same column name but different table in custom db query

Modify your query and use the SQL alias as:

$my_row = $wpdb_c->get_results("SELECT Employee.Name as Employe_Name, Area.Name as 
Area_Name, Area.Region as Area_Region FROM Area INNER JOIN Employee ON Area.ID = 
Employee.Area_ID WHERE Employee.ID = " . get_the_ID());

Then in your code use:

$my_row[0]->Area_Name