If I understand correctly, you seem to be looking for Product Variants in Shopify.
So that would be a single product with multiple variants, and then you should be able to select each Variant option in the dropdown.
You can see variants for each product in the Shopify Admin, when you open the Product.
As far as I know, you cannot really join multiple different Products to display on the same Product page in dropdown options, it would need to be single product with variants.
So I would suggest starting by creating some products with variants and seeing how it then looks on the product page.
If the product does not have any variants currently, then you can enable and create them here on the Products Admin page:
If you already have different Products that you would like to merge into Products with Variants, you can look into using our app Matrixify for that.
Here we have a great tutorial on how to group products into products with variants.
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