Change Display Email Name

Change Display Email Name

I am sure this has been asked many times, but I don't know what keywords to search in order to find my answer.
So I'm trying to switch from gmail to zoho, so I signed up under my gmail address, but I wanted to use a different name here. 
So my email for gmail is nrjensen11, but here I signed up under RainJensen. 
When I send an email to someone, I would like it to show up in their inbox as "Rain" or "Rain Jensen," but even though I changed my user profile name to "Rain," my emails are still showing up as NrJensen11. 


How do I change it so that all emails show up as "Rain" for people? 
Also, is there any way that I can get the top of my  https://personal.zoho.com to stop displaying my gmail address? 


How can I get that to say either just Rain or my zoho.com account? 

I'm trying to get AWAY from gmail, why is this being so difficult?