Usernames and t.me
Official telegram.org Source
You can set apublicusername on Telegram. It then becomes possible for other users to find you by that username – you will appear in search under 'global results'. Please note that people who find you will be able to send you messages, even if they don't know your number. If you are not comfortable with this, we advise against setting a username on Telegram.
You can set up a username in Settings and use the universal search box in the chat list to search for chats, messages, and usernames.
Official Telegram Reference: https://telegram.org/faq
Part of the TGWAY.com Official Telegram Knowledge Base (98 Verified Q&As).