2 added 231 characters in body
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Deep down the function uses get_comment_author_link() to output the author name. That function is filterable. Inside the function it checks if the author has a URL and wraps the name in a link to it if it exists. We can use the get_comment_author_link filter to just output the name, and ignore the URL. This is pretty simple, since the callback for this filter gets the author name as one of its arguments, so we just need to pass it through untouched:

function wpse_284352_author_link( $author_link, $author ) {
    return $author;
}
add_filter( 'get_comment_author_link', 'wpse_284352_author_link', 10, 2 );

EDIT: It's actually even simpler, the URL has its own filter, which means that can be filtered with one of WordPress' built in functions in one line:

add_filter( 'get_comment_author_url', '__return_empty_string' );

Deep down the function uses get_comment_author_link() to output the author name. That function is filterable. Inside the function it checks if the author has a URL and wraps the name in a link to it if it exists. We can use the get_comment_author_link filter to just output the name, and ignore the URL. This is pretty simple, since the callback for this filter gets the author name as one of its arguments, so we just need to pass it through untouched:

function wpse_284352_author_link( $author_link, $author ) {
    return $author;
}
add_filter( 'get_comment_author_link', 'wpse_284352_author_link', 10, 2 );

Deep down the function uses get_comment_author_link() to output the author name. That function is filterable. Inside the function it checks if the author has a URL and wraps the name in a link to it if it exists. We can use the get_comment_author_link filter to just output the name, and ignore the URL. This is pretty simple, since the callback for this filter gets the author name as one of its arguments, so we just need to pass it through untouched:

function wpse_284352_author_link( $author_link, $author ) {
    return $author;
}
add_filter( 'get_comment_author_link', 'wpse_284352_author_link', 10, 2 );

EDIT: It's actually even simpler, the URL has its own filter, which means that can be filtered with one of WordPress' built in functions in one line:

add_filter( 'get_comment_author_url', '__return_empty_string' );
1
source | link

Deep down the function uses get_comment_author_link() to output the author name. That function is filterable. Inside the function it checks if the author has a URL and wraps the name in a link to it if it exists. We can use the get_comment_author_link filter to just output the name, and ignore the URL. This is pretty simple, since the callback for this filter gets the author name as one of its arguments, so we just need to pass it through untouched:

function wpse_284352_author_link( $author_link, $author ) {
    return $author;
}
add_filter( 'get_comment_author_link', 'wpse_284352_author_link', 10, 2 );