Below is a sample list of blocks available for editing with wp.blocks.registerBlockStyle.
All the following blocks needs to be prefixed with core/:
'core/archives' 'core/audio' 'core/buttons' 'core/button' 'core/calendar' 'core/categories' 'core/classic' 'core/code' 'core/column' - A single column within a columns block 'core/columns' - The columns wrapper 'core/cover' 'core/file' 'core/gallery' 'core/heading' 'core/html' 'core/image' 'core/latest-comments' 'core/latest-posts' 'core/list' 'core/media-text' 'core/more' 'core/navigation' 'core/navigation-link' 'core/nextpage' - The page break 'core/paragraph' 'core/preformatted' 'core/pullquote' 'core/quote' 'core/rss' 'core/search' 'core/separator' 'core/social-link' 'core/social-links' 'core/more' 'core/spacer' 'core/tag-cloud' 'core/table' 'core/verse' 'core/video'
Note that the embed blocks are exceptions. Prepare yourself for a long list:
'core/embed' 'core-embed/wordpress' 'core-embed/spotify' 'core-embed/twitter' 'core-embed/youtube' 'core-embed/facebook' 'core-embed/instagram' 'core-embed/soundcloud' 'core-embed/flickr' 'core-embed/vimeo' 'core-embed/amazon-kindle' 'core-embed/animoto' 'core-embed/cloudup' 'core-embed/collegehumor' 'core-embed/crowdsignal' 'core-embed/dailymotion' 'core-embed/hulu' 'core-embed/imgur' 'core-embed/issuu' 'core-embed/kickstarter' 'core-embed/meetup-com' 'core-embed/mixcloud' 'core-embed/reddit' 'core-embed/reverbnation' 'core-embed/screencast' 'core-embed/scribd' 'core-embed/slideshare' 'core-embed/smugmug' 'core-embed/speaker-deck' 'core-embed/ted' 'core-embed/tumblr' 'core-embed/videopress' 'core-embed/wordpress-tv'
Full site editing blocks:
'site-title' 'site-tagline' 'site-logo' 'template-part' 'post-title' 'post-content' 'post-author' 'post-comments' 'post-comments-count' 'post-comments-form' 'post-date' 'post-excerpt' 'post-featured-image' 'post-tags' 'post-terms' 'query-title' 'loginout'