You can allow people who have a community account to post ideas anonymously. Posting as a guest can be useful when people in the community might be influenced in their voting by knowing who is posting. With this enabled, new ideas will display a check box through which someone can post anonymously.
You can allow guests to post ideas by using the admin console.
Admin Console: Ideas > Idea Settings > General
To allow guest user posts, on the General page of the admin console select the Allow registered users to post as guest users check box.