Can the ViewBag name be the same as the Model property name in a DropDownList?

You should not use the same name for the model property and the ViewBag property (and ideally you should not be using ViewBag at all, but rather a view model with a IEnumerable<SelectListItem> property).

When using @Html.DropDownListFor(m => m.CustomerId, ....) the first "Please Select" option will always be selected even if the value of the model property has been set and matches one of the options. The reason is that the method first generates a new IEnumerable<SelectListItem> based on the one you have supplied in order to set the value of the Selected property. In order to set the Selected property, it reads the value of CustomerID from ViewData, and the first one it finds is "IEnumerable<SelectListItem>" (not the value of the model property) and cannot match that string with any of your options, so the first option is selected (because something has to be).

When using @Html.DropDownList("CustomerId", ....), no data-val-* attributes will be generated and you will not get any client side validation

Refer this DotNetFiddle showing a comparison of possible use cases. Only by using different names for the model property and the ViewBag property will it all work correctly.

There is not harm to use it. You will not get any error. but best practice is to bind model property.