How do I concatenate only if not null in SQL Server?

You could simply use NULLIF() as the following:

SELECT NULLIF(CONCAT('A', Id), 'A') Id,
       Name
FROM
(
  VALUES
  (10, 'Mike'),
  (NULL, 'Jane')
) T(Id, Name);

OR

SELECT TT.Value Id,
       T.Name
FROM
(
  VALUES
  (10, 'Mike'),
  (NULL, 'Jane')
) T(Id, Name) CROSS APPLY(VALUES (NULLIF(CONCAT('A', Id), 'A'))) TT(Value);

The function CONCAT() will returns 'A' if the Id column is NULL, thus you need just to check if it returns 'A' using NULLIF() function which will returns NULL if the concatenated string = A.

You could also use CASE expression if you which to as:

SELECT CASE WHEN TT.Value <> 'A' THEN Value END Id,
       T.Name
FROM
(
  VALUES
  (10, 'Mike'),
  (NULL, 'Jane')
) T(Id, Name) CROSS APPLY(VALUES (CONCAT('A', Id))) TT(Value);

You can try like the below code to get your expected solution:

Select 'A' + convert(varchar(255), id) AS id, name
from PeronTable;

Here is a sample screenshot :

Hmmm. You can use + instead of concat():

select 'A' + convert(varchar(255), id), name
from t;

convert() (or cast()) is necessary assuming that id is a number and not a string.

+ returns NULL if any argument is NULL; concat() ignores NULL arguments.

Of course, you can use concat() with a case expression:

select (case when id is not null then concat('A', id) end), name
from t;