From the FAQ on their site:

Frequently Asked Questions

1. What happened?On October 16, 2019, Register.com determined that a third-party gained unauthorized access to a limited number of our computer systems in late August 2019, and as a result, account information may have been accessed. No credit card data was compromised as a result of this incident.
2. What are you doing about it?Upon discovery, we took immediate steps to stop the intrusion. We promptly engaged a leading independent cybersecurity firm to investigate and determine the scope of the incident. We notified the proper authorities and began working with federal law enforcement.

   We are notifying affected customers through email and via our website, and as an additional precaution are requiring all users to reset their account passwords.

3. What data/information was involved?Our investigation indicates that account information for current and former Register.com customers may have been accessed. This information includes contact details such as name, address, phone numbers, email address and information about the services that we offer to a given account holder.

   We encrypt credit card numbers and no credit card data was compromised as a result of this incident.

4. What can I do to protect my account?We have already taken additional steps to secure your account, and there is nothing you need to do at this time. The next time you log in to your account you will be required to reset your password.

   As with any online service or platform, it is also good security practice to change your password often and use a unique password for each service.

5. Is my credit card information at risk?We store credit card numbers in a PCI (Payment Card Industry) compliant encryption standard and do not believe your credit card information is vulnerable as a specific result of this incident. That said, it is good practice to monitor your credit card account and we encourage you to notify your credit card provider if you see any suspicious charges.
6. Should I reset my password as part of this?We have already taken additional steps to secure your account, and there is nothing you need to do at this time. The next time you log in to your account you will be required to reset your password.

   As with any online service or platform, it is good security practice to change your password often and use a unique password for each service.