A hoodie with a zipper is generally referred to as a zip-up hoodie. On the other hand, a hoodie without a zipper is called a pullover hoodie. While there are many names for similar garments in English, these two terms are widely used and understood. Other terms that have been suggested for a hoodie with a zipper include zip-up and full zip hoodie. However, these terms are not as commonly used as zip-up hoodie. It is worth noting that a jumper is another name for a hoodie without a zipper.