What does "SMS Messaging Account" mean in Hangouts? I'm using Nexus 5. In my Hangouts settings, I noticed that the setting called "Default SMS Messaging Account" was set to my email address with my full name (And can alternatively be changed to "SMS" instead, which hides previous chats)

Does this mean that I've been broadcasting my full name and email address to everyone I sent "SMSes" to?
It is a weird and confusing design decision in my opinion. 

To answer your question : No. Your full name and email address is only 
linked to your Google account and is only used for your Hangout chat.