how do you leave a backlink on a site like this?

http://www.smallbizsurvival.com/2012/08/choosing-website-name-whats-different.html

I tried all the options to leave a comment (Google Account, WordPress, AIM, TypePad, etc.) but I can't figure out how to use my own anchor text and URL instead of the the URL of the site that I used to login (like WordPress, TypePad, etc.).

"Anonymous comments are off temporarily due to a huge wave of anonymous spam. You will need to log in with any Google, Gmail, or Open ID account to comment. "

Also: http://www.smallbizsurvival.com/p/commenting-policy.html

It's likely the owner is either: blacklisted you or is using automated filtering techniques

A registered google account will do the trick, and make sure your comment is decent and related to the blogs theme as the blog is moderated.

Your anchored text is considered as a spam and that's all. Usually blog moderators remove such comments if only such comments are REALLY topic related and provide useful links and information. In other cases they are removed relentlessly.