There are a handful of ways to do this. If you are using the modern Garmin Connect...
Click the three horizontal bar icon on the left edge of the screen.
Click the word Activities.
Click Quick Edit.
Update the fields (Privacy, Favorite, Name, Activity Type, Course, Event Type) as appropriate.
Click Finish.
If you are in the activity details page, you can...
Click the Pencil icon at the far left of the icon bar.
Choose Quick Edit.
Update the fields (Name, Activity Type, Event Type, Course, Description) as appropriate.
Click Finish.
If you have an activities widget on your dashboard that is configured to show a recent activity, you can click the Pencil icon next to the activity name, modify the name, and then click the check mark.