Churchteams links the phone number being used to the person signing up during a registration.
It is likely that in the past you have registered a friend or family member for an event or signed them up for a class at your church. The texting feature in Churchteams links the mobile phone number to one person based on the first time that person is set up in the system. Once that number is linked to the other person, they aren't able to use text-to-register for themselves and your phone number will be linked to their name.
Trying to have two people use the same phone for texting purposes (at least features that involve registering or giving) is not recommended. Any person living outside your household should always register themselves in order to avoid associating your mobile number with their profile. One exception to this is with the multi-person registration. The person who owns the phone MUST be the first person to register and then you can register others after that.
To reset a phone number, text the word END to your Text-to-Church number. This will clear out any previously linked information and you can then re-register.