I have recently replaced my old domain with a new one, I have made the new domain as primary domain in Shopify DNS setting.
However, when I tried to do Google search using my new shop name, some of the pages still showed under the old URL with the old domains. (although they seemed to be redirected correctly).
Is there any way I can fix this and have all search results displaying the new domain?
your old pages are in google cash ang google bot didn't visit your site, thats why you have old domain results. SE dont know you got new domain. Go to webmaster tools and submit a mirror for your site or just wait for a couple weeks.