So recently something changed and users no longer have the option to enter their names when voting for a server.

There is only one option now :

"Daily Server Vote"

"Submit Vote"

Where did the dialog to enter the players name go?

It used to be like this
https://i.imgur.com/KxtNx3n.jpg
and now it's like this
https://i.imgur.com/d8ghUhj.jpg

There is no option for players to enter their names.