Hi, @pug26! I recently saw your post here and see you marked this as solved. I wanted to drop in here to ensure that helpful resources are shared in case others may encounter the same trouble with the domain they purchased.
It sounds like you may have trouble with a domain that has a typo when you purchased it or you may have some trouble with your search results online.
If there was a typo in your domain, you should contact us right away to make sure you have that corrected. Before any purchase the system will want you to confirm that the correct domain is being bought, however, we understand if you were in a rush and missed checking your typed domain before purchase. Our team can help you if this is something that you're encountering.
We have a guide to help you understand how domain purchases work on Shopify.
You mentioned that you were on Google doing a search. Google will show you the results for millions of other websites no matter what you type in. If you typed in "BOWTIQUE", it'll show you results from all over the internet, not just the exact word you typed. This doesn't mean that your site will show up first as there is a chance that someone else in the world has a similar business name or has a longer history of having a website with a similar word.
To help you better understand search engines I found a guide to help you out. Shopify has a guide on SEO as well so that you can better optimize your own site to show up on search engines. Remember that it can take time for your site to show up on the first page of Google search results. This is normal.
I strongly recommend this free tutorial here to help with all the basics of SEO related to your domain and search engines.
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