home phone doesn't display name with number for names in the directory

What make and model of phone and what service?

AT&T DL72219, according to the manual, any number within the phone's directory should display the name and number when receiving a call from that person.  It does, but just for one of the 19 listings.

That most likely works off caller id, so make sure you have the phone number in the directory the same as what caller id is is showing.

Per the manual:

You might need to change how a caller ID number is saved in the directory if the entry does not appear in the correct
format. Caller ID numbers might appear with an area code that is not necessary for local calls, or without a 1 that is
necessary for long distance calls. For details, see View dialing options on page 68.

Most of the numbers are cell phone numbers meaning we have to dial the 1 plus the 10 digits. I've tried leaving off the 1 and still no go.

Per the information provided the CID must be the same in the directory as what you get when called.  Is it?  Doesn't matter what you have to dial, what matters is what's displayed when you receive the call. 

I've tried entering the number in the directory exactly as displayed when the calls come in.  Still no good, I even used the process of transferring the displayed number directly into the directory and adding the name but it still doesn't work.

Memory match
If the incoming telephone number matches the last 7 digits of a telephone
number in your directory, the name that appears on the screen matches the
corresponding name in your directory.
For example, if Christine Smith calls, her name appears as Chris if this is how
you entered it into your directory

OK so this is what I found on what you're saying.  If it is not working as described call the number in the troubleshooting section.  Do you have any of the call blocking features activated?  If so try turning call blocking off.  If nothing you tried works your only recourse is to call the trouble number. 

You are talking calls coming into your phone number and not calls coming into a cell number you have paired with the phone system.  Correct?  That's the only other thing I can think of.  I'm sure you've scrolled through the directory many times to check both name and number are there. 

I'm starting to think I have a faulty set and you are right, I haven't even tried to link up a cell phone. One thing at a time, I've a call into AT&T, hope they can either help or replace the units.