Google only chooses to index a website if there are links pointing to it's site address, or if you have manually submitted your site to them. (When someone links to your website, it counts as a "vote" in favor of your site, and so it tells search engines like Google that they should include it in their search results).
So - the first thing is to make sure you have no links from any other websites (including social accounts like blogs, facebook, twitter) that point to your IconoSites URL. If you have already submitted your IconoSites URL to the search engines, that's ok, just go ahead and submit your custom domain ASAP (Do that here - https://iconosites.zendesk.com/entries/20934311-how-to-add-your-website-to-search-engines).
For faster indexing, what you need to do is get some backlinks that point your custom domain (i.e. www.yoursite.com). Google already knows that both your IconoSites URL and your custom domain are pointing to the same website; however, when they detect more links pointing to your custom domain, they will know that this is the site address that YOU want them to include in their results. And, at a certain point, they will unlist the other address (in this case, your IconoSites URL) that has little to no links pointing to it when compared to the other. It's as simple as that.
So you should start by placing links directly to your custom domain from your blog, twitter, or any accounts that you have. Feel free to link directly to the inner pages of your website (i.e. any other page besides your home page), as "deep linking" will help speed up the process.
Once you have done these things, give it anywhere from 3-6 weeks and google will update their results and the change should be reflected. It may take longer, depending on how many conflicting links you have -- but keep in mind that all of this is entirely up to Google.
If you have any further questions, post a question in the Google Webmaster Forum.