How do I submit my website name to search engines?

Answer 1

Look no further than “Search Engine Watch”.
Here’s their free online search engine marketing guide.
http://searchenginewatch.com/showPage.html?page=2156221

You’ll find the major search engines that are the most
important places to be listed. With each listing you’ll
find a section titled, “Getting Listed” that gives you
step by step instructions on how to properly submit your
site’s information to each individual search engine.

Answer 2

Google, for instance


http://www.google.com/webmasters/

Submit your site to be scanned by the google bot, and if you're using wordpress, then you can download a plugin and have it create sitemaps to submit to google every time you post a new entry so google knows everything about your site. (nooks and cranies)