How does renaming or deleting a custom field affect reports?

What is the consequence of deleting or renaming a custom field on reporting?

Changing a custom field name in turn changes the Analytics data model to rename the related data item. This changes the query item path that was embedded in the query specifications when the report was created from the original package with the original data item name. 

Similarly, deleting a custom field deletes it from the Analytics data model.

This causes an expression parsing error for reports still referring to the original custom field's data item name and will require a change in the report design to reflect the new data model.