The name on the browser has nothing to do with it. DoubleClick and others of its ilk don't check to see if it's Firefox. But thanks to Firefox's extensions, or add-ons, cookies are very easy to control without having to go into the preferences.
I use an extension called Prefbar — click on the thumbnail
in this post and check the top of the picture. Prefbar might need tweaking to work because it wasn't updated (maybe it has been, by now), but you can turn cookies on and off with PrefButtons, as well. PrefBar and PrefButtons have other controls, as well, that I haven't bothered with because of other extensions or simply don't apply. And there are other Firefox add-ons that easily control cookies.
Adblock is a godsend, along with automatic updaters that block all DoubleClick's ads, along with the other international cookie-tracing outfits like it, and any other ad you don't want to see.
Since Firefox is cross-platform, these extensions work on PCs, as well.