What is JotForm?
JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
At JotForm, we want to make sure that you’re getting the online form builder help that you need. Our friendly customer support team is available 24/7.
We believe that if one user has a question, there could be more users who may have the same question. This is why many of our support forum threads are public and available to be searched and viewed. If you’d like help immediately, feel free to search for a similar question, or submit your question or concern.
We have a widget that lets you save a home screen icon for iOS devices: http://widgets.jotform.com/widget/add_to_home_screen. Unfortunately, I'm not sure if this will prompt you to select a custom icon.
A workaround would be to use icon changer apps:
This will allow you to change the icon in your Android/iOS devices. The only downside is you cannot publish the same to your end-users.