From the remarks in the sp_rename definition:
Renaming a stored procedure, function, view, or trigger will not change the name of the corresponding object name in the definition column of the sys.sql_modules catalog view. Therefore, we recommend that sp_rename not be used to rename these object types. Instead, drop and re-create the object with its new name.
A computed columns, from what I learned (maybe I am wrong), is kind of a function.
The QotD was on "sp_rename", not "Alter" table and nothing in the definition talked about "error", so I got it wrong... 🙁