MySQL 5.7

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create table A( `key` int );
create table B( `key` int, name varchar(25) );
insert into A values(1),(2);

Records: 2  Duplicates: 0  Warnings: 0

insert into B values(1,'John'),(1,'Michael'),(2,'Alice'),(2,'Josh');

Records: 4  Duplicates: 0  Warnings: 0

-- Your original case :
SELECT A.key, GROUP_CONCAT(B.name SEPARATOR ', ') 
    FROM A LEFT JOIN B ON A.key = B.key 
    WHERE B.name = 'John'
    GROUP BY A.key
    
key
GROUP_CONCAT(B.name SEPARATOR ', ')

1
John

SELECT A.key, GROUP_CONCAT(B.name ORDER BY B.name SEPARATOR ', ') as "Names"
  FROM A 
  LEFT JOIN B ON A.key = B.key 
 WHERE EXISTS ( SELECT 1 FROM B WHERE name = 'John' AND B.key = A.key )
 GROUP BY A.key
 
key
Names

1
John, Michael