Nick here from Shopify.
Can I ask what login information you are referring to exactly please? I don't see why that would be an issue other than you possibly getting confused or mixed up with the same login for some stores. It might be a good idea to delete one store first and then create the new one to avoid this. But other than having two different .myshopify.com URL's there should be no problem with having the same login details under the same email.
Something which you might also find useful is the Shopify multi-store login allowing you to switch between Shopify stores which are associated with the same email address. You can read more about that here.
Hope that helps!
All the best, Nick