Agreed that this is the correct way to go, but here's a scenario that I'm currently experiencing and am really put off google and gmail because of it.
My gmail account is used for all personal stuff. I've synced my phone, contacts, calendar, music, documents, to it. My Facebook, Twitter, tumblr, Instagram etc are also with this account
Over a week ago google disable my gmail account die to suspicious activity. I mailed them countless times as I hardly use that account and the only explanation I have is that I clicked on a shared file from my boss thinking it was work, when in actual fact it was a suspicious file.
I have had no feedback from google and do t know if I will ever recover my account and now my phone is doing the same. Shows names and number in contacts, but when they SMS, whatsapp or call I only see numbers. I've list so much information that I'm seriously considering never using any google apps ever again