fix: Revert changes to fix name updation from pre-chat form (#4741)

app/controllers/api/v1/widget/base_controller.rb

@@ -54,6 +54,7 @@ class Api::V1::Widget::BaseController < ApplicationController
       ).perform
     else
       @contact.update!(email: email)
+      update_contact_name
     end
   end
 
@@ -67,9 +68,14 @@ class Api::V1::Widget::BaseController < ApplicationController
       ).perform
     else
       @contact.update!(phone_number: phone_number)
+      update_contact_name
     end
   end
 
+  def update_contact_name
+    @contact.update!(name: contact_name) if contact_name.present?
+  end
+
   def contact_email
     permitted_params.dig(:contact, :email)&.downcase
   end