Your suspicion was correct; mysql_BE6F is not the name of the database but rather a unique ID which Indigo assigned to your MySQL service instance when it was created, for internal purposes.
Your MySQL service will initially contains no databases at all; I would suggest using an app such as Sequel Ace to log into the MySQL service and create your empty database(s) as needed.
Just one complexity somewhat unique to Indigo is that each MySQL service has a port assigned to it, which may not be the typical 3306 (Indigo allows multiple MySQL servers, and only one at a time can operate on any given port). You can find this information inside Indigo, eg port 50005 in this example:
I have not used EE before but hope the following "Server Address" will work for you:
127.0.0.1:50005 (replacing the port with that actually in use in your case).
Hope that makes sense — let me know! 🙂
