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This is a privacy issue. The only way you can get a sure answer is by seeking a lawyer.
However, here's my personal view (IANAL - I am not a lawyer and TINLA - this is not legal advice): full names are part of the public domain. It should be, as it's main purpose is for it to be a unique identifier in the daily interaction with your surroundings. This is also why providing a false name to authorities is illegal in most cases.
Protecting one's privacy is part of any website's responsibility. But this should go as far as possible, and use publicly available information such as a full name in combination with a photo, only if it fits the purpose of the website. If so, joining that website means you agree to provide your public information on the website for that purpose.
You will have to decide if it fits the purpose of your website, and inform your members of this consequence (and perhaps debate how far the consequences should reach). If they don't agree, they're free to leave. Or, alternatively, you can change the policy.
Herko