If you still have the old domain you can forward that domain to the new domain with a permanent redirect 301

If you are already running under the new domain name for your oxwall site remember that the old link data stored in the database for newsfeed will have to be changed to the new domain unless you want it to use the redirect.

Many newsfeed content links are hard coded inside the database tables (i dont know why oxwall developers did that, it was a dumb thing to do)  So that means if you have the redirect set up, and someone clicks on one of those old newsfeed items, it has to leave your new site, go to the old site, then get redirected back to your site, and depending on your server security, and htaccess, it may not load, it may cause issues.

You may have to go into the database and manually change every single hard coded url in every single content record. 

You may want to ask patricia, she may have found or developed a process to do this quicker, she is very good at that... :)

I have never changed the domain, but what I have done many, many times is to copy a complete website together with its database in another domain to test with real data from hundreds or thousands of users. After copying everything completely, I cancel the functions of sending emails and I can test plugins without risk and with real data, such as the one I developed that eliminates old private messages. It would have been a disaster if something had gone wrong and deleted valid unread messages, for example.

In these tests I have never found invalid links anywhere, except if I have changed an https web to http or vice versa.

But it seems to me that what "O" asks is about the positioning of the web in the Google search engine ... I am afraid that with this change it will have gone from the position in which it was to the last of the last because Google will understand that they are two different websites. It is never a good idea to change the domain name, and it does not matter if they are similar or completely different.