Currently, when Adding a Shortcut to the Home Screen (Menu > Add to Home Screen), there is a pop-up opportunity to Rename the Shortcut as desired prior to dropping it onto the Home Screen. This helps to keep your Shortcuts orderly and meaningful.
However, when Installing a Web App (Menu > Install), the option to Rename the Shortcut does not exist.
As it stands now, FireFox/Android grabs the default name from the Web App. If you have multiple Web Apps from the same Web Site, they all get named the same on your Home Screen. For example, if you have multiple Dashboards in SharpTools, they all get named "SharpTools.io", thus creating confusion when trying to open the desired Dashboard with one click.
In contrast, Chrome currently offers a pop-up to Rename the Shortcut when both Adding Shortcuts or Installing Web Apps on the Home Screen.
Please consider a pop-up opportunity to Rename the Shortcut as desired when Installing Web Apps prior to dropping it on the Home Screen.