Stored procedure expects a parameter I am already passing in

I am trying to execute a stored procedure with this declaration:

ALTER PROCEDURE [dbo].[getByName]
    @firstName varchar,
    @lastName varchar
AS
...

And I am calling in C# as follows:

public List<Person> GetPersonByName(string first, string last)
{
    var people = new List<Person>();
    var connString = ConfigurationManager.ConnectionStrings["MyDbConnString"].ConnectionString;
    using (var conn = new SqlConnection(connString))
    {
        using (var cmd = new SqlCommand("dbo.getByName",conn))
        {
            cmd.CommandType = CommandType.StoredProcedure;
            cmd.Parameters.Add(new SqlParameter("@firstName", SqlDbType.VarChar, 50)).Value = first;
            cmd.Parameters.Add(new SqlParameter("@lastName", SqlDbType.VarChar, 50)).Value = last;
            conn.Open();
            using (var reader = cmd.ExecuteReader())
            {
                people = ReadPeopleData(reader);
            }
            conn.Close();
        }
    }
    return people;
}

But I just get back this error:

Procedure or function 'getByName' expects parameter '@firstName' which was not supplied.

Update:

ALTER PROCEDURE [dbo].[getEmployeesByName]
    @firstName varchar(50),
    @lastName varchar(50)
AS
...

and stating:

cmd.Parameters.Add(new SqlParameter("@firstName", SqlDbType.VarChar, 50)).Value

for both parameters, yet it continues to throw the exception.