Thank you for writing.
PropertyGridTextBoxEditor is based on RadTextBox and does not offer auto-complete functionality. You can use a PropertyGridDropDownListEditor with AutoCompleteMode - Append and DropDownStyle set to DropDown. If you want to you can go and hide the drop down button which will make the editor look more like a text box.
Another option is to create a custom editor based on RadAutoCompleteBox. You can find more information on this approach in our online documentation - Using Custom Editors.
I hope this is useful. Should you have further questions, I would be glad to help.
the Telerik team