Where's your web address listed?
If you're using outside channels to direct traffic to your website, eg. you have your web address on your Facebook page, you need to update the address there.
The main areas to consider are:
Not updating your Google Analytics tracking could result in a loss of traffic data.
If you've got a 301 redirect setup, those landing on your site via a directory will still land on your website, but without a redirect they'll see a 404 page. So make sure you've updated any directories your website is registered with.
Register and Verify your new domain with
Doing so can help you understand how Google views your site and optimise its performance in search results.
With the ever growing popularity of Social Media, customers may be finding your Facebook page before your website. Because of this, it's important to make sure you've got the correct URL on your Social Media profiles.
Many people will look at your email signature for contact details. Keep your signature updated with the new web address.
Without a 301 redirect on your old domain, it's crucial that you get your Van Signage, business cards and any leaflets updated so your customers aren't directed to a broken page.