Mapping new domain name

I have registered a new domain name through wordpress.
The old one is https://www.m4bmarketingblog.com (which will expire soon)and the new one is https://www.m4bmarketing.com

I was told that all I had to do was go into the wordpress.com domain setting page and select the new domain name as the primary one and it would automatically map all files to the new domain name. This did not occur. The site only appears with words not the design etc

I changed in wordpress general settings the wordpress url and blog url to the new name as well as in php manager.

Have I done this wrong or do I have to go through the steps as in the following link, which I do not actually understand as I have no experience with this.

https://codex.www.ads-software.com/Changing_The_Site_URL#Domain_Name_Change

Any help would be really appreciated.

Thanks
Susan