Sp_rename fails with

Msg 15248, Level 11, State 1, Procedure sp_rename, Line 357

Either the parameter @objname is ambiguous or the claimed @objtype (object) is wrong.

You would get this error if you have ‘DOT’ in between your constraint name. SP_rename fails because object_id(ContraintnamewithDOT) returns NULL for constraint objects with DOT (.) in their name.

Solution

Drop and recreate the constraint without DOT (.) in name.