How do I add a new custom format while making a post in WordPress?
The default formats are standard, aside, image, gallery... I want to add a new format of 'xyz' name. How can I do it?
New formats cannot be introduced by themes or even plugins.
Wordpress currently supports only few post formats, you can have a look at all Supported Post Format on codex. If you are looking for format which in not mentioned there, you will have to use the categories or tags conditions to customize the look for that posts.
As of May 2013, Post Formats are being pulled from the basic core download. You might check out a plugin although I've searched for one and haven't seen one. I know Alex King has an older one from 2011.
Either use the current post formats, and make custom template for them. Or, make custom post types, but, switching post types seems to be a huge pain in the ass.