I currently have this left join as part of a query:
LEFT JOIN movies t3 ON t1.movie_id = t3.movie_id AND t3.popularity = 0
The trouble is that
The error is clear -- you just need to create an alias for the subquery following its closing ) and use it in your ON clause since every table, derived or real, must have its own identifier. Then, you'll need to include movie_id in the subquery's select list to be able to join on it.   Since the subquery already includes WHERE popularity = 0, you don't need to include it in the join's ON clause.
LEFT JOIN (
  SELECT
    movie_id, 
    movie_name 
  FROM movies 
  WHERE popularity = 0
  ORDER BY movie_name
  LIMIT 1
) the_alias ON t1.movie_id = the_alias.movie_id
If you are using one of these columns in the outer SELECT, reference it via the_alias.movie_name for example.
To get one per group to join against, you can use an aggregate MAX() or MIN() on the movie_id and group it in the subquery. No subquery LIMIT is then necessary -- you'll receive the first movie_id per name withMIN() or the last with MAX().
LEFT JOIN (
  SELECT
    movie_name,
    MIN(movie_id) AS movie_id
  FROM movies
  WHERE popularity = 0
  GROUP BY movie_name
) the_alias ON t1.movie_id = the_alias.movie_id