It depends. While some dating services do require you to submit a copy of your ID to participate (helping prevent fake/inaccurate profiles, catfishing, dating scams, etc.), it's a good idea to make sure the service and website are legitimate before providing any information.
Once you've verified that a service is legitimate, if you're also concerned about how it might share or use your ID information, it might help to look at the service's privacy policy and see what options you have and who you can contact with further questions.