Rebranding our app and implications ?

Shopify Partner
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I hope you can help with this. I am currently making updates to my app and I have plans of re-branding it after the many improvements. 


I would like to know if, after I rebrand the app -- which also will need to update the app's urls in the app setup section -- Will the app remain installed on the user's shopify end ? or will it disappear from their apps list.  Any other technical implications that I should be aware of?  


I would much appreciate your feedback