I feel the replacement patterns are quite lackluster as of now. The best pattern for recognizing where a database is from is currently 'hostname' - which in cases of SSH tunneling is usually just '127.0.0.1'. Not useful at all like you can imagine.
I propose introducing a new pattern which will use the name/label (Session name) that you've saved for the server/connection.
(This feels like such an obvious pattern it should already exist - so if it does - it needs to be added to the mouseover-label for the textfield)