It's important to consider SEO before moving to a new domain name. If you don't, you risk the SEO value in your old domain being lost.
The Plug in SEO Plus Broken Links checker can help to recover some of these, but it's much better to plan a clean SEO migration too.
If both your old domain and new domain are on the same Shopify store, this is a simple case of changing your primary domain in your Shopify admin. All of the relevant permanent redirects are created automatically.
We can advise you for no extra charge about how to migrate cleanly from your old domain to the new without losing SEO. Send details of the migration you'd like to do to firstname.lastname@example.org.