This depends on the phone. This is one of those nuances that separates the OS experience between manufacturers. First try seeing if there is an option to do it in the edit contact panel under notifications.
Alternatively, you can use a diff texting app that gives you more options. I use Textra. You press and hold a convo and choose settings from the menu button and then go to notifications and then pick one.
Keep in mind that not all android phones have the same options so your phone may not have the option built in to the native messaging app. Mine does but I still like Textra.
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