There is not an option to select a custom wedding website URL that does not contain the "www.mywedding.com" domain name.
However, you may keep your mywedding.com domain URL and purchase any available custom domain URL that you would like. Then, you can set your new custom domain URL to redirect to your wedding website.
At this time, we don't sell or register alternate domain names. You could try selecting a unique URL from a domain registrar like Go Daddy www.godaddy.com or eNom www.enom.com and then purchase it.
Once you have purchased the domain, you will be able to direct it to your current mywedding.com address - www.mywedding.com/yourchosenURLhere. For that you'll need to contact the tech/customer support department for the company from which you decide to purchase your domain. Linking the domain to the website is not something we can do from our end.
Finally, web hosts (such as godaddy.com or enom.com) might ask for “nameserver” or IP/DNS information, but the only information that is needed in order to redirect your new custom domain name is the address that you have chosen for your wedding website. If you should be requested to provide this information, please reply to the tech support department at whichever company you chose to inform them that MyWedding doesn't release any DNS/nameserver or IP information.