Strava has segments which are displayed under the ride timeline chart as you move the marker. If you change the name of the activity then Intervals.icu will receive the update.
Garmin Connect provides the raw .fit files which contain additional data not supplied by Strava (left right power balance, running power, power meter used, lots of other things). Intervals.icu will soon have support for visualising that data. Garmin does not supply the activity name. So if you change that in Garmin Connect you also have to change it in Intervals.icu.
If Strava revokes Intervals.icu API access or discontinues their API then I have to delete all of your Strava data from Intervals.icu. Strava are no longer granting rate limit increases to apps which means they are currently following a “Strava apps must die” strategy.
If you do enable Garmin Connect support duplicate Strava activities will be replaced with Garmin ones. Thats currently a little buggy so sometimes you might need to delete the Strava one manually.