You can set up a public username on Telegram. It then becomes possible for other users to find you by that username — you will appear in contacts search under ‘global results’. This allows to message you without needing to know your number. Public channels and groups can also have usernames.

More in our FAQ:
https://telegram.org/faq#usernames-and-telegram-me

If you mention usernames in Telegram messages, they become a link that opens the conversation, group, or channel. Like this: @username (yes, this example is a little recursive 😁).

You can also use usernames outside of Telegram with the help of Telegram.me. Like this:
https://telegram.me/username

For some reason, you can also use this:
https://telegram.dog/username

Don't ask. 🐺