Selecting data from multiple rows and insert it into a column

This should work:

-- Query every name_changes where rownum <= per group limit (2)
select * from (
    -- subquery for attaching rownumber counter for `name:city` groups
    select `date`, name, city , old_mul, new_mul, 
        case when @lag != concat(name, ':', city) then @rownum:=1 else @rownum:=@rownum+1 end as rownum, 
        @lag:=concat(name, ':', city)
    from name_changes,
    -- init values
    (select @rownum:=0) init_rownum, 
    (select @lag:=null) init_la
    order by name, city, d desc
) numbered
where rownum <= 2;

I had a previous answer about mimicking window functions in mysql: How do I write this query? where I explained this in more details.

Following what's already written at How to use GROUP_CONCAT in a CONCAT in mysql...

Let's assume you have a schema and sample data equivalent to:

CREATE TABLE properties
(
    id integer PRIMARY KEY,
    property varchar(255) NOT NULL
) ;

CREATE TABLE recommended_providers
(
   id integer PRIMARY KEY,
   recommended_provider_name varchar(255) NOT NULL
) ;

CREATE TABLE properties_recommended_providers
(
   prop_id INTEGER NOT NULL REFERENCES properties(id),
   recommended_provider_id INTEGER NOT NULL REFERENCES providers(id),
   PRIMARY KEY (prop_id, recommended_provider_id)
) ;

INSERT INTO properties
VALUES (1, 'property 1'), (2, 'property 2') ;

INSERT INTO recommended_providers
VALUES (1, 'provider 1'), (2, 'provider 2'), (3, 'provider 3');

INSERT INTO properties_recommended_providers
VALUES (1, 1), (1, 2), (2, 3) ;

You can either have:

SELECT
  p.id AS property_id, property, 
  GROUP_CONCAT(recommended_provider_name SEPARATOR ', ') AS provider_names
FROM
  properties p
  LEFT JOIN properties_recommended_providers pr ON pr.prop_id = p.id
  LEFT JOIN recommended_providers rp ON rp.id = pr.recommended_provider_id
GROUP BY
  property_id
ORDER BY
  property_id ;

(Check it at SQL Fiddle)

or

SELECT
  p.id AS property_id, property, 
  (SELECT
      GROUP_CONCAT(recommended_provider_name SEPARATOR ', ')  
   FROM
       properties_recommended_providers pr
       LEFT JOIN recommended_providers rp ON rp.id =
                                         pr.recommended_provider_id
   WHERE
       pr.prop_id = p.id
   ORDER BY
       /* You can easily order by in this case */
       recommended_provider_name
   ) AS provider_names
FROM
  properties p
ORDER BY
  property_id ;

You can check the second one at SQL Fiddle