No you cannot change this here any and you can’t change this at Facebook or anywhere else either. In order to use he WordPress.com like button one has to have a WordPress.com username account and be logged in.
That being said I wouldn’t place a high value on like’s. They don’t amount to anything more that bragging stats. For clarity likes and shares numbers are misleading when you consider page view stats. Your followers and anyone with a WordPress.com blog who is logged into WordPress.com can “like” and “share” your posts in several locations such as the Reader without ever clicking into your blog and creating a page view stat. Those who have username accounts only but no blog can become followers and click the “like” and/or “share” buttons. http://onecoolsitebloggingtips.com/2012/07/09/wordpress-followers-likes-and-stats/
Note: To compel readers to click into my blog to read the full post thereby creating a page view stat, I have set my RSS Feed for posts to “summary” on this page > Settings > Reading