I am wondering if I can change the application name of a connection in SQL Server itself, e.g. in the logon trigger? Is that possible or is the application name "read only"?

Edit to explain the motivation: I would like to mark all audited connections in my logon trigger, so that I write only one record per connection through its many logon events. I thought I could modify some info, e.g. the app name, of a connection so that next time around the logon trigger sees that it can ignore this connection attempt because it already logged the info around this connection (like user, host etc.).