A minimal reproducible example is not provided. Shooting from the hip.

Notable points:

• CROSS APPLY is producing a generic XML regardless of the table structure.
• XQuery FLWOR expression is composing a precise desired XML output.

Overall, the answer is following the same minimal reproducible example pattern. You copy it to SSMS as-is, and it is working.

SQL

-- DDL and sample data population, start
DECLARE @tbl TABLE (ID INT IDENTITY PRIMARY KEY, FirstName VARCHAR(20), LastName VARCHAR(20));
INSERT @tbl (FirstName, LastName) VALUES
('Fred', 'Smith'),
('Anna', 'Polack');
-- DDL and sample data population, end

SELECT ID
    , x.query('for $x in /root/*
        return <Answer name="{local-name($x)}">
          <value>{data($x)}</value>
        </Answer>') AS Result
FROM @tbl AS t
CROSS APPLY (SELECT t.* FOR XML PATH(''), TYPE, ROOT('root')) AS t1(x);

Output

+----+--------------------------------------------------------------------------------------------------------------------------------------------------------+
| ID |                                                                         Result                                                                         |
+----+--------------------------------------------------------------------------------------------------------------------------------------------------------+
|  1 | <Answer name="ID"><value>1</value></Answer><Answer name="FirstName"><value>Fred</value></Answer><Answer name="LastName"><value>Smith</value></Answer>  |
|  2 | <Answer name="ID"><value>2</value></Answer><Answer name="FirstName"><value>Anna</value></Answer><Answer name="LastName"><value>Polack</value></Answer> |
+----+--------------------------------------------------------------------------------------------------------------------------------------------------------+