How to subscribe a person to a telegram bot?

Question

Messengers

There is a bot, people add it to themselves and use the functionality. I want to add the ability to subscribe to certain events on the site, which each user has their own. How to identify a user?
I see it like this:
1) The user adds our bot to his telegram
2) The user on the site enters his nickname from the telegram (thus connecting the account on the site with the account in telegram)
3) I save information about all chats in the database, I find the desired chat by nickname and send information there.
Everything would be fine, but looking through the databases, I found that many users do not have a nickname and my scheme stops working.
How to do everything right?