contacts show up as numbers instead of names why ?

I have an IPhone4S (service provided by Veriizon - Model#MF259LL/A - IOS 8.4) and for some odd reason a call or text woul come in showing a number not a name of people/persons that I know I have in my contact list.

Got a new phone because it was still under warranty, went to store where I bought it and they were nice enough to tansfer info into new phone. Results good for a little while back to same situation. Long story short been back to store several times to restore, did a number of restores at home with techfrom apple and up until today phone does not work to my satisfaction. I also have another strange problem where phone is set to vibrate/tone on text and sometimes I just get vibrate, strange. I always update software when notified so I have latest IOS in phone. Very dissapointed in Apple products and if I could I would get rid of my phone but right now it would cost a lot so I will just have to wait for my upgrade to come. Thanks for your time looking forward to hearing from you and maybe you can come up with a solution to my problem.