You don't change a doamin name you just get a new one. When you buy a domain name it is yours until it expires or you sell it. It is easier to just get another. Go to godaay.com for really great pricing on domain names.
The best thing to do for right now would be, register the new domain then point the old domain to it. That way anyone that had the site bookmarked still can find you. The redirect page should state that they are being redirected and please bookmark the new page.
Given that a domain name is only USD $10/year, any good host will let you host more than one domain without additional cost (especially if you're re-directing and not fully hosting), and the domain must have had some merit in order for you to register it in the first place...
I'd just register the new domain, and have the old domain redirect to the new one at the server level (i.e. none of that unprofessional "please update your bookmarks" crap - if the user types in domaina.com it just loads domainb.com with no intervening pages). Just keep the old domain as a legacy domain. If you sell one shirt a year from that domain, you've justified retaining it.
I think the whole idea was to get rid of the first domain and start a new one. Thus the reasoning for redirect and please update crap. I myself when I see I am being redirected WITH NO WARNING, close out the site and move on. I dont like when sites hide behind redirects. But if you want to have 100 domains and pay for them all just to redirect to a single go right ahead. Kind of defeats the getting a new domain up and running if they keep the old one just to redirect.
The point is not losing the customers who have the old url, which could easily be worth a measly $10/year. People pay a lot more for mail forwarding and telephone redirection.
And if the re-direct is done serverside you won't even notice you're being redirected (and therefore close the window) - you'll just arrive at the site you expected to, but with a different URL. If you're redirecting with HTML you're doing it wrong.
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