SEO implications for site with changed URL

[DorsetJoomla]

I have built a Joomla website for a client and now the client has decided to change his domain name. I thought that the easiest way to do this was to make the new domain an alias of the website and change any references to the old domain name within the website. So I did this and it all seems to work OK. I have even registered the new name with Google my businesses. Now, do I need to do anything to the site settings to ensure that the new domain name gets picked up OK ? I have implemented OSmap for a site map.
The site is still accessible from the old domain name incidentally.
Thanks for any suggestions.

[pe7er]

On the old site I would create HTTP "301 Moved Permanently" status codes for all old URLs and point them to the new domain. Search engines will update their search index accordingly.

If the structure of the URLs on the new site are incidental to the old site, then a couple of lines in your .htaccess are sufficient. Otherwise you can add a list of all your old individual URLs + new URLs + 301 redirect.

Info: https://en.wikipedia.org/wiki/HTTP_301

[DorsetJoomla]

Thanks for your response but I think you are missing the point that it's actually the same site, nothing has moved to a new site. All I have done is add an alias to the original site and URL . So far everything seems to work OK (except that sending emails via the "new" domain name is proving unreliable despite updating the configuration file details). My question really is about SEO optimisation in this situation.

Thanks