Sometimes businesses change names and brands re-brand - it's perfectly normal.
If this happens to you or your business, it might also be time to change your website's domain name. After all, you can't very well carry on using www.theneatfreak.com when you've just renamed your business Corey Cleans.
But hold up! Before you make the switch, there are some very serious implications to changing your website's URL - some pertaining to SEO.
Here's what you should consider with regards to how SEO can be potentially impacted when you change domains - namely, your links.
Check your internal links
When you switch domain names, one of the first things you should do is configure a 301 redirect so that all instances of your old URL automatically direct to the new URL. Additionally, you should change the URL in your WordPress settings (assuming you have a WordPress-backed website).
Then, you should manually check all internal links on your website to ensure that links to your website have been updated to reflect the new URL. Usually this should automatically be taken care of when you make the configurations mentioned above, but just in case any instances were missed you should double check all internal links. If you catch any that haven't been updated, go ahead and update the link yourself.
Ensuring that your links aren't broken is extremely important for SEO, as Google penalises sites with broken links. Plus, broken links negatively impact a site's usability and can cause a visitor to get lost within its pages.
Check your backlinks
Don't forget about links to your site that exist on other websites!
Backlinks are absolutely HUGE when it comes to SEO juice. A link to your site on another related site of high(er) authority can help immensely in increasing your search rankings. It would be a shame to lose this after changing your domain name.
So what do you do, then?
First, find out which sites are linking to your old domain. There are many tools out there that can tell you this, including Moz's Backlinks and Small SEO Tools' Backlinks. You could also log into Google Webmaster Tools, click on Search Traffic, then click Links To Your Site.
Then, start contacting those sites and politely asking if they wouldn't mind changing the link to reflect your new URL. Consider throwing a "thank you" in there as well for linking to your site in the first place, so they know you really appreciate it.