Hi Matt,
Depending of the version of the plugin and BBB you are using, it may be either impossible or as as as cclicking on the name/description to edit it.
Lets start with, where the name/description is stored.
When the meeting is created, as you noticed, the name of the activity is passed to BBB as the name of the meeting, along with a buch of other information like the version of moodle you have, the version of the plugin, the context (or course) etc. All that information is part of the recording archive as metadata, so whatever change you do to the Activity in Moodle won;t affect the passed recordings, only the new ones.
Until BBB 1.0/BigBlueButtonBN 2.2.x it was not possible to change thos values. No through the plugin anyways.
I am assuming you are using v2.1.x. If this is the case, you have two options. You either update to 2.2.4 (the latest version) or you do it using an external tool called api-mate.
On BigBlueButtonBN 2.2.x you should see a little pencil next to the name (and description) for editing the name. Same as the icon shown for editing the name of the activity in Moodle (assuming that you are on 3.3 or newer).

I hope this helps. If it doesn;t send us the versions you have (all of them) and we may be able to give you a better advice.
Cheers,
Jesus Federico