Changing website link on google

Hello, 

I have had no help to solve my query so far. 

I am having trouble changing my website name on google. I have bought my domain name 'rosetteequinetransport.co.uk' and have uploaded it to the Web however after going into settings and changing the website name and meta description on search optimisation I have had no luck to change my website name appearing on google. 

My username on Adobe is Castillo it seems to have used that as my name. I changed it thinking it would solve the issue but no luck. It shouldnt have to use your adobe ID to publish a website name? something isnt working I need some guideance please.