Which canonical name is better? www or non-www?

It doesn't matter for SEO. The most important thing that you will always redirect to one and only instance so crawler bots won't count by mistake www.a.com/index.html and a.com/index.html as double content even though modern bots can detect it is the same site and the same page of it. Without www. it is easier for user to write in address bar and easier to remember. I would go for a.com instead of www.a.com. Once you add both to your server, make proper redirection using IIS proper settings or .htaccess file on Apache. Afterwards add website to Google Webmaster tools and other common web analysis systems while it is important to set default domain in there. Set it without www. !

Good luck

To some extent the answer to this question depends on your audience. More technical websites like to drop the www, such as jQuery.com and (of course) stackoverflow.com

If your website is intended for an average home user, they tend to expect the www at the start of the web address and you may cause confusion and possibly even dis-trust if you fail to include it.

The most important thing is that your website works both with and without (preferably redirecting to your preferred option as people may share a link to the page you are on and search engines need to know the true "source" of the page), but think about your audience when you decide which to use.

IMO, non WWW is better for blogs/personal sites etc.....and WWW is good for company sites, orgs etc...