If you need to rename a constraint after creating with typo or due to any other reason, you could follow the below steps.
--creating test table with PK constraint
CREATE TABLE dbo.RenameConstraintTest
(
ID int CONSTRAINT PKC_RenameConstraintTest PRIMARY KEY CLUSTERED
)
GO
--check the existance of the constraint
SELECT * FROM sys.key_constraints WHERE name='PKC_RenameConstraintTest'
GO
--rename the constraint
EXEC sp_rename N'[dbo].[RenameConstraintTest].[PKC_RenameConstraintTest]', N'PKC_RenameConstraintTest2', N'INDEX'
GO
--check the old constraint
SELECT * FROM sys.key_constraints WHERE name='PKC_RenameConstraintTest'
GO
--check the renamed constraint
SELECT * FROM sys.key_constraints WHERE name='PKC_RenameConstraintTest2'
GO