The specified delivery date/time is shown in shipping method's name for informational purposes only to let customers know how long they should wait for the order to arrive. Shipping Table Rates extension is unable to provide the options of delivery date selection from customer's side, or automatic delivery date calculation.
If you'd like to add estimated delivery time to the shipping method name, navigate to Sales → Shipping Table Rates → your shipping method → Methods and Rates → your rate and fill in the 'Estimated Delivery (days)' column with the necessary values for each rate:
Once done, go to the General tab of your shipping method, insert {day} variable in Name field, and click Save:
As a result, the estimated delivery time of the suitable shipping rate will be displayed in the name of the shipping method:
Since module version 1.13.0 we added a new {interval} variable to display the delivery interval. The functionality is available as a part of an active product subscription or support subscription.
The {interval} variable, allows specifying the delivery interval in the method. When you use a new variable in the method name, the interval calculated based on the value from Estimated Delivery (days). The interval value is calculated using the example: “tomorrow - the day after tomorrow + the number of specified days” (if today is December 7 and 5 days are specified in Estimated Delivery (days), then the method will display “December 8 - December 13”). This functionality works based on the store's locale, not the customer's locale: