Olvid is a messaging service from France which is useable without a phone number and accessible under Android and iOS (which allows running it on a tablet without a SIM-Card). It provides an end-to-end encryption which includes metadata and thereby can assure anonymity of its users.

Threema is an instant messaging app from Switzerland with Apps for iOS, Android, Windows, macOS and Linux. The communication is end-to-end encrypted and the apps are open source.
The app can be downloaded here:

• App Store
• Play Store