SqlCommand.Parameters.Add not converting parameters when trying to do DELETE statement

I am doing an INSERT query to a db with the following code which works fine.

public int InsertPerson(Person person, out string errormsg)
{
    SqlConnection dbConnection = new SqlConnection();

    dbConnection.ConnectionString = @"Data Source=(localdb)\mssqllocaldb;Initial Catalog=PersonDB;Integrated Security=True";

    String sqlstring = "INSERT INTO PersonTable ( FirstName, LastName ) VALUES ( @firstname, @lastname )";
    SqlCommand dbCommand = new SqlCommand(sqlstring, dbConnection);

    dbCommand.Parameters.Add("FirstName", SqlDbType.NVarChar, 30).Value = person.FirstName;
    dbCommand.Parameters.Add("LastName", SqlDbType.NVarChar, 30).Value = person.LastName;

    try
    {
        dbConnection.Open();
        
        int i = 0;
        i = dbCommand.ExecuteNonQuery();
        
        if (i == 1) 
        { 
            errormsg = ""; 
        }
        else
        {
            errormsg = "Could not add person";
        }

        return i;
    }
    catch (Exception e)
    {
        errormsg = e.Message;
        return 0;
    }
    finally
    {
        dbConnection.Close();
    }
}

However when I try to use the logic in a DELETE query it does not convert the @firstname and @lastname to the parameter values passed to the method call.

public int DeletePerson(Person person, out string errormsg)
{
    SqlConnection dbConnection = new SqlConnection();

    dbConnection.ConnectionString = @"Data Source=(localdb)\mssqllocaldb;Initial Catalog=PersonDB;Integrated Security=True";

    String sqlstring = "DELETE FROM PersonTable WHERE FirstName = @firstname AND LastName = @lastname";

    SqlCommand dbCommand = new SqlCommand(sqlstring, dbConnection);

    dbCommand.Parameters.Add("FirstName", SqlDbType.NVarChar, 30).Value = person.FirstName;
    dbCommand.Parameters.Add("LastName", SqlDbType.NVarChar, 30).Value = person.LastName;

    try
    {
        dbConnection.Open();
        int i = 0;
        i = dbCommand.ExecuteNonQuery();

        if (i == 1)
        {
            errormsg = "";
        }
        else
        {
            //errormsg = "Could not delete person";
            errormsg = sqlstring;
        }

        return i;
    }
    catch (Exception e)
    {
        errormsg = e.Message;
        return 0;
    }
    finally
    {
        dbConnection.Close();
    }
}

The query that is created from the DELETE method looks like this DELETE FROM PersonTable WHERE FirstName = @firstname AND LastName = @lastname

It works fine when I hardcode the SQL query but not when I use the attributes of the Person parameter as parts of the query..