I\'ve done something like this in order to use on duplicate key update:
CREATE UNIQUE INDEX blah on mytable(my_col_to_make_an_index);
You are correct. The index name is only used as an identifier, so you can refer to it if you need to edit, delete or query on it later. It isn't used for any other purpose.
You can name the index whatever is most convenient for you, but some consistency would probably help you (naming your index 'blah' is perfectly valid, but you won't have a clue where it is, what it does, or why you created it).