Editor warning: This solution is computationally inefficient and may bring down your connection for a large table.
NB - You need to do this first on a test copy of your table!
When I did it, I found that unless I also included AND n1.id <> n2.id, it deleted every row in the table.
If you want to keep the row with the lowest id value:
DELETE n1 FROM names n1, names n2 WHERE n1.id > n2.id AND n1.name = n2.name
If you want to keep the row with the highest id value:
DELETE n1 FROM names n1, names n2 WHERE n1.id < n2.id AND n1.name = n2.name
I used this method in MySQL 5.1
Not sure about other versions.
Update: Since people Googling for removing duplicates end up here
Although the OP's question is about DELETE, please be advised that using INSERT and DISTINCT is much faster. For a database with 8 million rows, the below query took 13 minutes, while using DELETE, it took more than 2 hours and yet didn't complete.
INSERT INTO tempTableName(cellId,attributeId,entityRowId,value)
SELECT DISTINCT cellId,attributeId,entityRowId,value
FROM tableName;