Here’s a relatively easy way to automatically remove “session” from your export filenames:
Create a new pair of range markers, and give the range whatever name you’d like your export file to have. (Usually, I’ll use the session name or a song title.) Move the range markers to your session start and end points, or whatever span you’d like to export.
When you export your session, select this range as the time span, rather than the default “session”. Leave the Session Name checkbox unchecked, and this should give you a nice, clean filename that you won’t have to mess with every time.
Ardour should remember this setting for subsequent exports, at least until you close the session, so you’ll only have to do this once.