Open a text in your conversation list, tap the 3 dot icon in the upper right, choose personalize.
I will tell you from experience if you get more than 1 that are a different icon the last one in will be what shows up when you wake your phone. What I found worked better for me was do the above method to personalize but I chose individual text tones for certain contacts, that way when I hear the tone I decide whether to bother waking the phone ,or not, and checking the message. It's right handy to know if the text is from the wife,a child of mine, my brother, etc or just a random one from another source.
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