I just had this same problem. Here is how I solved it. I went to another sheet in the workbook and made the list of names that I wanted in the dropdown list. Once the names were entered I highlighted them all and clicked on Insert, then Name, and then define. I gave the list of names a name "Customers". Just above the list of names, I put this same text so that I would remember what I called it.
Now you can switch back to the sheet that you were working on, and click on a cell that you want the dropdown list to appear. Click Data, and then Validation. From the dropdown under allow, select list. Under source enter and equal sign and then the exact text that you entered in the previous step "=Customers". Hit OK and the dropdown arrow will appear every time that you highlight that cell. The nice thing is that you can copy this cell and paste it as many times as you would like. If you go back to the original sheet where you entered all of the names, and add a name, it will appear wherever you pasted that cell in the other sheet.
Hope this helps
Jeff