iPhone 5s: texts and calls show numbers instead of names
Put people in your iPhone contacts, when you put people in the Contacts application it is best to put in the full telephone number and the country of the person then the iPhone will use the telephone number formatting of that country.

I live in the Netherlands and I have setup my iPhone as such, when I create a new contact by default (unless I change the country) they are listed as being in the Netherlands. The country code for the Netherlands is +31, the "+" is the convention for country code.

If I type in a mobile phone number (the prefix code for mobiles is '6') say 
+31 6 12345678 then the iPhone will format it that way. If I type in a fixed land line number, say +31 40 1234567 then it will put in the spaces to correctly identify the region code '40'. If I put in other people from other countries with other formats for phone numbers, say +1 123 12345678 for something in the US, the iPhone will automatically put in the correct spacing.

And you will see the person's name, not number, for incoming and outgoing calls.