Zotero allows you to easily create folders in order to organize your research citations.
Click the "New Collection..." button on the upper left side of your Zotero pane to create a new folder. Simply drag and drop your resources into the appropriate folder. This is a great way to organize your research sources according to particular assignments/projects that you're working on.
Your list of folders will be automatically alphabetized. If you'd like items to appear at the top of the list don't aren't alphabetically at the top, you right click on the folder and choose "Rename." This will allow you to add a special character such as an asterisk (*) to make sure the item appears at the top of your folder list.
If you have a PDF file that's arbitrarily named with the number from a given database (as seen above), right click on the PDF with your Zotero library and choose "Rename File from Parent Metadata." Zotero will take the associated metadata from the original resource and rename the PDF for you.