I'm still kind of new at the Mint, but I looked into this recently and hope this answer will be helpful.
In the interest of simplicity I'm going to assume you're using pluma because it's installed by default.
In Pluma select Open. In the window that comes up use the left pane to navigate to your home directory. Right click in the home directory area and from the context menu choose "Show Hidden Files". Go into the .linuxmint/mintMenu/applications.list this is where your favorites menu configuration is stored. As a good practice, always save a backup copy before you edit any configuration file. You might already know that and I apologize if so, but I assume someone else might read this at some point and I think it always deserves mentioning. So choose Save As from the file menu and save it under a different name then reopen the original. You can add a new separator by adding a line called separator (you'll see it already done in the file). You can also move program shortcuts around and basically do what you like. Once you've got everything organized how you want, save the file and close pluma. Right click the "Menu" and select "Reload Plugins". Alternatively, if you're comfortable editing with vi, vim, nano or some other command line text editor you can navigate there in the command line and edit then follow the same "Reload Plugins" step.
To edit the text simply right click and go to the "Properties" and you'll see the text displayed for the program in the bottom.