This add-on was just what I wanted! You can name windows and it remembers it across restarts. The context menu is on the web page so it works great with tab management sidebars and hidden Firefox tab bar (such as with Tree Style Tabs). Also the context menu doesn't just allow you to send the current tab to another window it also allows you to switch focus to another window which is really useful since I have my windows on different Virtual Desktops!

One thing I would like to be added though is the ability to change the order of the windows in the context menu and sidebar so that they followed a more logical order.

Edit:
Performance heavy on startup when restoring sessions with many tabs. I have over 1000 tabs open and this issue means that I have had to disable the extension. I would really like to use it but Firefox can't restore my session at startup with this extension enabled. I have opened an issue on GitHub for this problem. Good extension otherwise though and this is not really a problem most would notice.