The name is great, as is the slack command /screen, just keep using it. Saying this as a user of GNU Screen. It's OK, approximately nobody is going to be confused by this in the real world.
Do you really think nobody is going to be confused when you tell them to use "Screen"?
"I'm staring at my screen right now, what do you mean?"
"It's the name of an app".
If people have to introduce your app as "use the app called Screen", then it's a bad name. Think Viber, Skype, Whatsapp, Colgate, Facebook.