How to Pass Dependencies Through a GUI?

Alright I'm not sure if this is possible with MCreator or if it requires custom code, but here it is:
I have a GUI process I'm making for naming a mob. I'll use one particular mob as an example:
Step 1: Procedure that activates when a player right clicks on a fox. If player is holding taming food, the fox tames and it pulls up the GUI for the player

Step 2: Player types the name they want for the fox in the GUI textbox

Step 3: When player pushes the "Finished" button, procedure sets the fox's display name to whatever was typed, and then closes the GUI.

Problem I'm having is I don't think the GUI is passing the entity/source entity dependencies as I need it to. If I add "set display name to Test" in the Step 1 procedure, it works perfectly, because it knows Target Entity = that fox. When I put "set display name to Test" into Step 3, there is no name displayed above the fox.

I tried adding a "while this GUI is open tick" procedure that would pass entity and source entity from Step 1, but it won't let me link it to the GUI cause it's missing dependencies. Any ideas how I can get that fox entity dependency to pass through the GUI to Step 3?