This should go without saying, but if you seek customer support from a domain name company’s Twitter account, you should not share your account details publicly. Tweeting account numbers, domain name details, passwords, call-in pin codes, or any other information that could be used by a bad actor is unwise and potentially harmful. I recently saw someone do this, and it could a big time security issue.
Twitter can be a great way to get support when other methods have either failed or are taking too much time. Many of the medium and large domain industry companies have Twitter accounts that are either staffed by support team members or are used by people who can connect customers to the support team. These Twitter accounts want to resolve customer issues and probably want to keep issues private, while showing that the company offers top tier support. With that in mind, customers regularly reach out to companies via Twitter, and some may not think about the repercussions of sharing private account details.
From what I have seen, the best bet to getting quick customer support via Twitter may be to tweet to the company to let them know an issue needs to be resolved. Instead of sharing personal or account identifying details publicly, it makes more sense to either tweet the ticket number or take the support issue to Direct Message. Most accounts will need to message publicly first to get a follow-back, but this is not necessarily the case.
I think it is pretty obvious that private account details should never be shared publicly, especially when it comes to companies who manage domain names on behalf of others. It seems that people may not realize certain details are private and that exposing them could be a security risk. Twitter is a great way to get customer service, but people need to remember it is a public setting, and they wouldn’t share private account details in a public setting.