[Steve Swift]

I can't find my friend in contacts, either by looking through the list of contacts, or by searching for him. Fortunately he has a rare family name, so that helps.
If I try to add him as a new contact, then I'm told that the contact already exists, and indeed this is the case if I look at Google Contacts on my PC.
So, I've added him with his nickname rather than his full name.

How can I bring my S4 into line with everything else?

[Rukbat]

First make sure you're not overlooking a leading space or dot in the name. The contact may be there, just in the wrong place.

Then make sure the S4 is syncing contacts, then sync.

If that doesn't fix it, delete all your contacts on the phone when it's off-line - no wifi, no mobile data. Then put it online and let it sync. (If all your contacts disappear in Google Contacts, hit More, then Restore contacts. (You can restore anything deleted within the past 30 days.)

[extraclass]

I had a name I couldn't find and it was listed under the persons business name. Amazingly search would not find the name!

[Steve Swift]

Thanks for the suggestions. I'll be out of range of network for the next couple of weeks, so I won't see anything beyond this, for a while.
I'll try the suggestions on my return.