while receiving a call, I do not see the name of the contact stored in the phonebook. What should be done?
That usually happens, when you use some kind of spam calls filtering app, such as for example the TrueCaller. If you use anything similar (on phones of some brands, it may be part of their OS), try disabling it to see whether it helps. If you manage to identify the app, contact its author and ask whether there is a way to forward the name to the system notification unchanged, in order that Garmin Connect can send it to your watch properly.
