You need to use a different email address for each store. All your other information can be the same, address, bank account, etc. You give the link to your other store in the Settings->About Your Store section. You need to choose a name no on else is using, including names you have used before but may not use now. Once a name has been used by anyone, you can't use it asgain.
If it is still rejecting it, make sure you are not using any of the words that the Etsy bots key on such as Amber, Ivory, names of endangered amimals, or copyrighted or trademarked phrases. You also can't use names of certain countries that have embargos in the US. If you have done all the rest pointed out above, it is probably some word you are using. Unfortunately, Etsy won't tell you what that might be.
Also, if your first store was suspended for whatever reason, any new store you try to open will be automatically rejected.
You don't need to link your shops until after the new store is approved. I added mine after I finally got the 2nd shop opened.
