This took me the longest time. It seems that you have to verify using another method from when you first verified both sites.
If this isn't the case for you, great! Just move on to the next step.
Here are two options I used:
Option 1: Add a meta tag to your new site's header
If you tried to do this to your old site after redirecting, you won't be able to because logging in will bring you to your new homepage or whatever page you entered into the Wildcard redirect at namecheap.
This was the case for me. So I only used this method for verifying my new site.
1. Under Appearance in the WordPress side menu, click Editor.
2. Click the file for your theme's header.
3. Under the <head> tag, paste the code provided by Google.
4. Click Update File.
5. Go back to the Change Site Address page to click on Confirm.
Option 2: Add a TXT record in Namecheap for your old site address
For most of us, this option is only valid for your old domain, because you need your new domain name servers to be the WA ones if you log in through WA.
1. At namecheap, under the old domain name, click Advanced DNS.
2. Go to Add Host Record.
3. Select TXT record from the drop down menu.
4. Enter @ for host.
5. Paste the code provided by Google for this TXT record in the value field.
6. Click Save Changes.
7. Go back to the Change Site Address page to click on Confirm. It can take 24 hours for the changes to take effect, so don't be alarmed if you can't confirm so soon.
Please be advised: All files and content (including database) on smartaboutit.com will be permanently deleted and overwritten by the new website. This cannot be undone, so please be sure that you want to overwrite all files and content on smartaboutit.com before proceeding. If there is any important Files on smartaboutit.com you may wish to back them up first.
I want to keep the same theme the same links and everything the same, the only thing I want to change is the name. What happens to the people that share my links, will the link not work anymore or will it redirect it to my new website name?