I tried EVERYTHING in this thread over the last few years. Nothing worked, I had to keep restarting the mail app to get the real mails isntead of the no sender ones. I even had another phone after my 5s. Now that I bought the 6 I had the same problem again. And this solution helped! I finally works! This way the contacts from your gmail are not included in the mailaccouont. Just add those seperately by creating a contacts account, use carddav, server gmall.com and your username and pw.
Thanks, finally I can use a very basic smartphone function (email) without issues!