I just changed my shop name by moving all of my yarn and plantable paper items to a new shop
http://www.ThoughtfulGemsCrafts.etsy.com from my original shop
http://www.craftsinbloomshop.etsy.com. As I agree with delightfulprints that you are not allowed to actually change your shop name, you can open a new shop, notify your existing customers from your original shop, list your items in the new shi\op and deactivate your listings in your original shop. The cons are that all of your feedback, hearts/favorites and sales numbers are associated with your original shop. It is almost like starting over again, but you do have an existing customer base that will follow you. It was a hard choice for me since I am new, but the original name was not my first choice. The new name coincides with my actual business name. Also, I just started listing items in my other shop, www.ThoughtfulGems.etsy.com. For me it was worth having consistent names. I just made the change. I hope this helps!