I'm having the exact same issue with my Pixel 3 and Alta HR. One of the reasons I bought it was to read my texts easily; knowing who it's from helps a bit, but ultimately isn't all that useful. I'm going to return the fitbit if I can't find a solution to this issue. It's a huge oversight not to support Google/Android's current flagship phone line that has been publicly released for over 9 months now.
I've tried various combination of toggling settings in my messenging service, fitbit app, permissions, bluetooth, etc, and nothing's bee working. Tried restarting my phone and the app a number of times as well. No luck. There's been some ambiguity among fitbit support in leading months about whether the Pixel 3 is supported (looks like it's "supported" by the app but not the device?) and the whole matter is just messy and inconsistent. Even when I'm connected, the syncing is unreliable as sometimes I will not be getting text notifications (not syncing) until I manually open the app and force a sync. This is why this isn't a functional product in my case. Best of luck and hope you can find a proper solution.
