No, you do not automatically own the Niche that you've suggested. Anyone with a Medium Reputation or higher can suggest a Niche. Once it is suggested, the Niche goes through the member approvals process via HQ/Approvals. If it is approved it will appear in HQ/Auctions.
Even if you are the one that suggested the Niche you will still have to bid on it, win the auction, then pay for the Niche. You will be notified by email if someone outbids you during the process. You can read more about the process here in the spec. You are reminded that the Niche you suggest goes up for public auction ( if approved) once you submit the Niche Suggestion form.
More information on the Auction process is here.