Customer is able to change the delivery date from My Account / My Orders section. You can enable this option on Global Delivery Settings

Allow Customer edit the delivery date #

The limit time user can edit is defined in the option "Delivery Date change Access Hrs." under the section Global delivery limits

Admin gets a notification by email with the requested change

Setup Business Weekdays and Business hours in addition to Delivery Weekdays>

How to show the estimated delivery date instead of choosing a date at checkout>