One workaround.
From your sp give a call to another sp in the target database and use sp_rename there.
/*sp in first database where column name has changed already*/
CREATE PROCEDURE dbo.a AS
exec northwind.dbo.a
GO
/*and in northwind put in code to change the name of column*/
CREATE PROCEDURE dbo.a AS
exec sp_rename 'Table.ColumnOldName',
'ColumnNewName' ,
'Column'
GO