How to customize captions in the 'Object Model' window when adding an item from the 'Customization' window?

You can use the GridEditorColumnChooserController.ColumnChooserExtenderChanged and ColumnChooserExtenderBase.ModelBrowserCreated events to implement this scenario:

C#
using DevExpress.ExpressApp;  
using DevExpress.ExpressApp.DC;  
using DevExpress.ExpressApp.Win.Controls;  
using DevExpress.ExpressApp.Win.SystemModule;  
using DevExpress.XtraTreeList;  
using DevExpress.XtraTreeList.Columns;  
using DevExpress.XtraTreeList.Nodes;  
using System;  
using System.Collections.Generic;  
using System.Linq;  
using System.Text;  
using System.Threading.Tasks;  

namespace XafApplication1.Module.Win.Controllers {  
    public class Controller1 : ViewController<ListView> {  
        GridEditorColumnChooserController gridEditorColumnChooserController;  

        private void ColumnChooserControllerBase_ColumnChooserExtenderChanged(object sender, ColumnChooserExtenderChangedEventArgs e) {  
            if(e.Extender != null) {  
                e.Extender.ModelBrowserCreated += Extender_ModelBrowserCreated;  
            }  
        }  
        private void Extender_ModelBrowserCreated(object sender, DevExpress.ExpressApp.Win.Editors.ModelBrowserCreatedEventArgs e) {  
            if (e.ModelBrowser != null && e.ModelBrowser.FieldsTreeList != null && e.ModelBrowser.FieldsTreeList.Columns.Count > 0) {  
                foreach (TreeListNode node in e.ModelBrowser.FieldsTreeList.Nodes) {  
                    UpdateDisplayName(e.ModelBrowser.FieldsTreeList.Nodes, e.ModelBrowser.FieldsTreeList.Columns[0]);  
                }  
            }  
        }  
        private void UpdateDisplayName(TreeListNodes nodes, TreeListColumn treeListColumn) {  
            foreach(TreeListNode node in nodes) {  
                string nodeValue = node.GetValue(treeListColumn) as string;  
                if(nodeValue == "Display Name") {  
                    node.SetValue(treeListColumn, "Custom Display Name");  
                    break;  
                }  
                UpdateDisplayName(node.Nodes, treeListColumn);  
            }  
        }  

        protected override void OnActivated() {  
            base.OnActivated();  
            gridEditorColumnChooserController = Frame.GetController<GridEditorColumnChooserController>();  
            if(gridEditorColumnChooserController != null) {  
                gridEditorColumnChooserController.ColumnChooserExtenderChanged += ColumnChooserControllerBase_ColumnChooserExtenderChanged;  
            }  
        }  

        protected override void OnDeactivated() {  
            gridEditorColumnChooserController = Frame.GetController<GridEditorColumnChooserController>();  
            if(gridEditorColumnChooserController != null) {  
                gridEditorColumnChooserController.ColumnChooserExtenderChanged -= ColumnChooserControllerBase_ColumnChooserExtenderChanged;  
                gridEditorColumnChooserController = null;  
            }  
            base.OnDeactivated();  
        }  
    }  
}  

See the attached project for more details.
See also:
- Tooltips in Object Model Popup of CustomizationForm
- TreeList.Nodes
- TreeListNode.GetValue
- TreeListNode.SetValue