Left Join with only one of multiple matches in the right table

I have a database, where every entry may have multiple names, therefore I made a name database. While all names will be displayed otherwhere I need a list of all main entries with one representative name. All names are ranked and the one with the highest ranking-position shall be used. Unranked names are “0” or “-1” and should be ignored and since the name-ranking-system is bad, the one to use is not always “1”. In the case of no name being there, the main entry should still be returned. In short: I need a left join that takes all entries of table “main” and joins them with the name that has the smallest, greater than 0, position, if there is one. main:

| main_ID | val_A | val_B |
+---------+-------+-------+
|       2 | some  | stuff |
|       3 | and   | more  |
|       4 | even  | more  |

names:

| name_ID | main_ID | name           | position |
+---------+---------+----------------+----------+
|       1 |       2 | best name      |        1 |
|       2 |       2 | some name      |        0 |
|       3 |       3 | alt name       |        3 |
|       4 |       2 | cool name      |        2 |
|       5 |       3 | abandoned name |       -1 |
|       6 |       3 | awesome name   |        2 |

what I want to get:

| main_ID | val_A | val_B | name         |
+---------+-------+-------+--------------+
|       2 | some  | stuff | best name    |
|       3 | and   | more  | awesome name |
|       4 | even  | more  |              |