Sync Telegram Contact with Phone Contact
I had the same issue on my Nexus 6P with Android 7.1, while it worked perfectly fine on another Nexus 6 with Android 7.0. Here's what helped:


reinstall the app (do not open yet)
go into Android Settings > Accounts > Telegram and enabled Contact sync
open the app and check Contacts


After this my contacts were synced as expected. No sure why the sync was off for me by default.