If you do not want your Quora profile and/or name to appear in search engines, go to your privacy settings page and set the option "Allow search engines to index your name?" to "No".
Unchecking this option will make Quora instruct search engines like Google not to index your profile page, and not to index your linked name anywhere else it appears on Quora, including answers you've written and any @-mention. In other words, if someone searches your name on Google, your answers and profile page should not appear in the results when you uncheck this option. Your name will show up as "Quora User" to any search engine crawlers that we detect, even on questions or answers that you contributed publicly (ie, not anonymously).
So if you're concerned about people being able to Google your name and have all your non-anonymous Quora answers or comments show up, this option provides some protection. On the other hand, if you think your public Quora answers add to your reputation and you want to maximize the number of people who see them, you won't want to use this.
For this setting to take effect, Google has to recrawl pages and update its index; we don't have control over how long this takes; in practice, it usually happens within 1–2 weeks.
Keep in mind that this privacy is just around your linked name as we display it on Quora. The content of all answers will be public and will be indexed by search engines.