Hi there AnnaandJess,
Thanks for joining us in Apple Support Communities. We understand you're seeing contact phone numbers instead of names when receiving a response to a text in Messages on your iPhone. We're glad you're here, and we'd like to learn more to see how we can help.
To begin, what type of account are you using for Contacts? Is this happening with iCloud Contacts or contacts from a third-party account? Learn more about the difference here:
Set up and use iCloud Contacts
Use other contact accounts on iPhone
Next, are you seeing this behavior with SMS/MMS text messages or iMessage? Have a look at this support article for more information:
About iMessage and SMS/MMS
Also, which iOS version is listed in Settings > General > About on your iPhone? If needed, this link provides details about how to update your iPhone:
Update your iPhone, iPad, or iPod touch
Send over these details, and we'll take a closer look from there.
Cheers.