How can I check field before selecting?

I have a table like this:

// Names
+----+--------+------------+
| id |  name  | visibility |
+----+--------+------------+
| 1  | Alex   | 1          |
| 2  | Jack   | 0          |
| 3  | Peter  | 1          |
+----+--------+------------+

I want to select name, but I need to check its visibility before selecting. In other word, I want it returns name if visibility is 1, and returns null if visibility is 0. How can I do that in the query?

SELECT (check visibility here) AS name FROM Names WHERE id = :id;

---

I can do that by PHP like this:

if ($result['visibility'] == 1) {
    $name = $result['name'];
} else {
    $name = null;
}

But I want to do that by pure-sql.