You can simply remove or add the domain from Admin Dashboard "Online Store -->> Domain".
Thanks and Regards,
I can only click on "manage" in this section. When I do this I have the option to "transfer domain" or change "dns settings" - or delete subdomains but I want the URL not be affiliated to the Shopify Store anymore.
In other posts online they said one should contact the support of Shopify but I can not find a mail or telephone number. Only the forum.
I have not tried to delete a domain on Shopify yet but I think it's impossible. Instead of deleting it, you can redirect (redirect 301 is better) it to your new domain and every time people access your old domain, they will be directed to your new domain. How to redirect? you can read this writing about creating URL redirect on Shopify.
Hope it helps!
Thanks for your message @Edward-Newgate - but I want the opposite. People that visiting the old URL should not get to my store. Instead, see a blank page or something. I will search the internet for more possibilities as my inquiry might be a little special.