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