If you would like to do it from ASA side by using ASDM, you have to create a client profile. When the client is connected to ASA, the profile will be pushed to the client.
The "connect to" should be populated from the client profile.
Per your previous post, you did not use client profile, I believe the current name in "connect to" box is the last host you successfully connected with. This name is saved in "preferences.xml" as I mentioned before. It could not be changed from ASA side but it only keeps the last host. So, if you can connect to the same host with a different name, the name in "preferences.xml" should be changed automatically.
