Discord will force all users to choose a new username: the usual number identifier is going to be removed.
Now Discord will have a system similar to Telegram or Twitter — each user will be asked to choose a new, unique username. The change will take effect in a couple of weeks, and how quickly you get the option to change your username will depend on the date you signed up for Discord. The longer you're on Discord, the sooner you can change your name.
The Discord blog states that users will now have a username and a Display Name. Display Names are being added so how you appear to other users stays the same. A unique alphanumeric username will be used only for connecting with other users (friending) and telling users apart when you check their profiles.
A non-unique Display Name that can include just about anything (including special characters, spaces, emojis and non-Latin characters) will be your most prominent form of identity. You can call it the Main Name and you will be able to change your Display Name whenever you want, even minute to minute.
You can find more information about these changes on the official Discord website.