Telegram 8.3 provides Anonymous posting in groups feature.
Some details are available in official Telegram blog here.

What is this?
Any group member which has purchased Premium can send messages signed not by his own Telegram name but by any of his channels (so they are called anonymous). If all conditions are met:

What are conditions?
You can send in group A messages signed by channel B name if all conditions are met together:
1. You use Telegram app or Plus Messenger app 8.3.0 or newer.
2. Group A is public or group A is linked to any channel as discussion group.
3. You are the owner of channel B.
4. B is public channel.
5. "Hide sender selector" mod is off.
6. Your channels are not banned in particular group (see details further).
7. You are Premium Telegram user.

How to send anonymous message?
1. Open group A.
2. Tap on your avatar on the left of input field.
3. Choose one of your channels.
4. Type the message and send id.

Can I restrict sending messages signed by channels in my group?
Telegram platform does not provide any way to restrict this for all group members at once. But you can restrict this to particular member if he has already send at least one message from one of his channels.
Do the following:
1. Tap near that message.
2. Tap on "Delete".
3. Tap on "Ban user".
Now that member is not able to send messages signed by his channels in this group. He will see icon for choosing one of his channels until he restarts app. After app restarting icon will not be displayed.
Please note: you won't know which member was that.

How to remove my avatar from input field?
App menu - Plus Settings - Messages - Hide sender selector.