You will have to create an index on that field and make it UNIQUE. That will stop duplicates being added.
To find existing duplicates:
SELECT name_id, count(name_id) FROM artists
GROUP BY name_id
HAVING count(name_id) > 1
will list all artists with more than 1 entry.
If you know how to use nested queries you can use this in a delete query to eliminate the duplicates - but this is complex sql and very easy to get wrong.
Best way, and foolproof. Create a duplicate table, but with the Unique index in place. Copy all the data from the first table into the second. All the duplicates will bounce off. Then rename the tables; and you also have a backup incase anything goes wrong with the second table.