You should add a custom plugin. That’s need a PHP main file that include, register a JavaScript file. The source below should result in an plugin. You find a usable solution also in the probs below.

PHP part

add_action( 'enqueue_block_editor_assets', 'my_gutenberg_scripts' );
function my_gutenberg_scripts() {

    wp_register_script(
        'my-editor-enhancement',
        plugins_url( 'editor.js', __FILE__ ),
        array( 'wp-blocks' ), // Necessary script handles.
        filemtime( plugins_url( 'editor.js', __FILE__ ) ),
        true
    );

    wp_enqueue_script( 'my-editor-enhancement' );
}

JavaScript part

In our example is this the code of the editor.js, that we enqueue above. The example add only one paragraph and two different heading types.

wp.domReady( () => {

    wp.blocks.registerBlockStyle( 'core/paragraph', {
        name: 'blue-paragraph',
        label: 'Blue Paragraph'
    } );

    wp.blocks.registerBlockStyle( 'core/heading', {
        name: 'default',
        label: 'Default',
        isDefault: true,
    } );

    wp.blocks.registerBlockStyle( 'core/heading', {
        name: 'alt',
        label: 'Alternate',
        isDefault: false,
    } );

} );

If you add isDefault: true, then this style will be marked as active on visible blocks that don’t already have a style specified.

core blocks

• core/paragraph
• core/image
• core/heading
• core/gallery
• core/list
• core/quote
• core/audio
• core/cover
• core/file
• core/video
• core/preformatted
• core/code
• core/freeform
• core/html
• core/pullquote
• core/table
• core/verse
• core/button
• core/columns
• core/media-text
• core/more
• core/nextpage
• core/separator
• core/spacer
• core/shortcode
• core/archives
• core/categories
• core/latest-comments
• core/latest-posts

Removing blocks

JavaScript part

 wp.domReady( () => {
    wp.blocks.unregisterBlockStyle( 'core/button', 'default' );
    wp.blocks.unregisterBlockStyle( 'core/button', 'outline' );
    wp.blocks.unregisterBlockStyle( 'core/button', 'squared' );
} );

Probs

• Automattic Block Style Example
• Bill Erikson great post.