Sorry, your account cannot be deleted, as stated by eBuddy themselves (e.g. on https://ebuddy.zendesk.com/entries/20265307-How-to-delete-eBuddy-ID- ).
Furthermore, good to learn this from their Terms: If you want to know which details eBuddy has recorded about you or if you want to change details which you cannot change in your account, you can contact our customer service via firstname.lastname@example.org. You can also request us to remove your personal details from our servers. Please note that we may be required by law to store the information we collect, even after you have terminated your use of the eBuddy Services.
For more info: http://www.ebuddy.com/en/privacy.html