There is an official Telegram app for the Apple Watch, but as 9to5Mac pointed out, it leaves a lot to be desired. You can't use the app independent of the iPhone, even on the cellular-enabled Apple Watch. And that's why developer Kosta Eleftheriou released Nanogram Messenger, which promises the complete experience on the Apple wearable.
Nanogram Messenger lets you view, send, and receive Telegram messages, whether your iPhone is nearby or not. If you're concerned about privacy, Eleftheriou says the app communicates directly with Telegram using its official SDK, and it doesn't collect any information.
The app integrates with Eleftheriou's other app, FlickType, a swipe keyboard designed for the Apple Watch. It'll make it much easier for you to type out messages with this gesture-based keyboard. Nanogram Messenger is available on the Apple Watch App Store for free.