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Don't associate a photo with that Contact entry? Leave that field blank.

I have some Contacts without photos. You have to add pix if you want them.
 
Google contacts will obtain a contact photo from the user if that user is also a gmail user and has added a photo. I don't think there's anything you can do about that.

Does iCloud do the same thing?
 
I haven't noticed Google doing that but I've added photos to my Contacts that are most personal to me and they would override your example.

Can't say about iCloud.
 
Only one account, with no picture it shows the first and last initial which I hate
 
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