Thank you SuzyQ for helping out. I appreciate you taking the time to help our fellow community members.
I'm not sure what you mean by sending a private text message. As SuzyQ mentioned, when sending a text message to another number only that person will receive your text message.
Are you referring to being able to send a text message from your phone to someone and not have your number appear as the sender and instead display as private? If this is the case, I apologize but this is not a function available on your phone.
However, if you are sending a text message to another Verizon Wireless number you can go to www.vtext.com to send a text message. The person will receive the text message and the sender will appear as anonymous. No number will appear and they will not be able to reply to the text message. There is no charge for this service.
I hope this information is helpful and answers your question. If this does not answer your question please post back and I'll be more than happy to further assist you.