Change Database Prefix to Improve Security?

It seems to be conventional wisdom that changing the default prefix for the WP database name is a very important step to reduce hacking. But is this actually true or is it a myth? I would be grateful to know to what degree this is a real concern. Are sites actually being compromised in large numbers by using the default name? As a followup question, are no negative implications for a site that uses a non-default db name? No problems with compatibility with themes, plugins, updates, etc?

Thanks very much