When you move to a new name, the old one carries traffic, links and recognition. Treat it as an asset to hand over, not to abandon. A domain that has been public for years has been linked from other sites, printed on cards, typed into phones and saved in bookmark folders that nobody will ever tidy.
A move done properly keeps most of that value. A move done carelessly sends it to the next person who registers the name.
What the old domain is carrying
There are four things to protect. First, inbound links from other websites, which pass visitors and also carry weight with search engines. Second, bookmarks and history in the browsers of people who already know you. Third, printed and spoken references: leaflets, vans, email signatures. Fourth, email. People still write to the old address, and if the domain lapses, so does the mailbox, and so does the chance to notice who was trying to reach you.
Make a short list of each before you start, and you will know afterwards what to check.
Redirect every address, not just the front door
Redirect every old address to its closest equivalent on the new site with a 301. The words "closest equivalent" matter. Sending every old URL to the new home page is the lazy version, and visitors who clicked a link to a specific page land somewhere unrelated and leave. Search engines tend to treat a blanket redirect to the home page as a weak signal for the individual pages.
If the new site keeps the same path structure, one rule does the job. On Apache with mod_rewrite, in the old domain's .htaccess:
RewriteEngine On
RewriteCond %{HTTP_HOST} ^(www\.)?example\.com$ [NC]
RewriteRule ^(.*)$ https://example.org/$1 [R=301,L]
If the structure changed, build a mapping table of old path to new path and load it as individual rules. Test the result with curl -I https://example.com/shop/ and look for the 301 status and the Location header.
Tell the search engines and the people
Inform search tools of the change of address. Google Search Console has a change-of-address tool for exactly this, and Bing Webmaster Tools offers something similar. Both want the old and new sites verified under the same account and the redirects already live. Submit the new sitemap at the same time.
Then tell people. Tell partners and update your own profiles: social accounts, directory listings, map listings, marketplace pages and the signature on every outgoing email. Ask the few sites that link to you most to change the link, which is better than relying on the redirect for ever.
Keep the old name registered
Keep the old domain registered for at least a year, ideally longer, because links and bookmarks take a long time to fade. Turn on auto-renew and put the renewal in the calendar. The fee is small next to the cost of someone else owning the address that thousands of pages still link to. Check that the nameservers and the redirect keep working; a registered domain with broken DNS is no help to anyone.
Email deserves its own line in the plan. Set up forwarding from the old addresses to the new mailboxes, or keep the old mail service running during the changeover, and reply from the new address so correspondents learn it. After a few months the forwarded volume tells you how many people have still not updated their address books.
Watch the logs
And watch the logs: they show which old addresses still draw visitors. A quick look at the access log tells you which pages deserve a better redirect, and when the traffic has dropped far enough to think about letting the name go:
awk '$9 == 301 {print $7}' access.log | sort | uniq -c | sort -rn | head -20
Also look for 404 responses on the old domain, which mean a redirect is missing.