Hi,
When Webex meeting is in progress and you start the recording, you don't get an option to name/rename the recording. You can initiate a feature request internally with Cisco Business Unit (from your profile it looks like you are Cisco Employee).
Once your recording is stopped, then you can login to your Webex account and rename the recorded file. Here are some screenshots:
Step-1: Login to Webex Account >> Go to Recordings
Step-2: Rename Recorded Meeting >> Save
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Thanks, Vaijanath S.