Anonymous accusations need to be handled with tact, discretion and care. Employers must investigate accusations of misconduct such as theft, harassment and discrimination even if they believe the accusations are false.

There is not a lot that you can do, but when you have any evidence of conversations or of other proof that disputes the lie, make sure you have it on hand. This can come in the form of slander, which is spoken defamation, or libel, which is harmful to one’s reputation through false written accusations. False accusations that are published in print or online are called "libel," while false accusations on television, radio, or in conversation are "slander." Consult a lawyer if you can afford to do so: under certain circumstances, you can bring a defamation case against the person falsely accusing … Being subjected to defamation can damage your job prospects, income, or standing in a community, so knowing how to deal with it is essential. Note: personally. Of course, the complaint could be about harassment, discrimination, or a safety problem – including a potential for workplace violence – and then the CEO should meet with you personally and let you know what she’s received. Defamation of Character in the Workplace Explained
If your business is is experiencing anonymous workplace complaints or you wish to ensure your policies are robust and that staff are aware of the policy regarding anonymous complaints, please contact us via phone (1300 227 901) or email for more information.

Your company will take seriously any gossip that implies you've done something wrong at work.

If you've been falsely accused of something at work, proceed with caution. My response to this: "I cannot defend myself against anonymous, generic accusations. Strong organization is often an effective defense against false accusations.
If the lie is something you feel might affect your standing with your job, it might be a good idea to talk to your boss about the situation.