It seems Samsung has removed this option for the included Contacts app (Googles app also does not support this, BTW) . However, you're not without options! Some (many?) messaging apps allow you to set notification sounds on a per-thread basis so once you have a conversation going with someone you can set that thread's sound and you're all set.
This has been a popular topic in here recently, we've had several threads on this (and the badges, BTW).
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