Depends on the app you're using for texting. If you're using Google Messages, you can just tap the three dots on a conversation and select Details. There you will see a Notifications section which will then let you customize that specific thread (it works for individual contacts or for group chats). I'd imagine it would be something similar if you're using Samsung Messages but I haven't used that in a while, so can't confirm. (Either way, the custom conversation should show up in the Notifications area for the messaging app as a separate notification category...)