Just the other day my displayed name changed from my full name (from Facebook login) to "Anonymous."
On all devices, web and 2 phones, it has stayed this way full time since then. Was changed just after I wrote to support for something unrelated.
I prefer this way, without my real, full name, which is very recognizable. In settings, shows both FB and GPlay accounts are connected.
Do I need to worry about losing access? Does support obscure names that are too distinct?