This looks like a default texting app (my LG's default is a green icon, but I think this will apply almost universally). Are you using another app by default for texts? I.e. I use Verizon Messages+ instead, Textra is popular, and I think Facebook Messenger (which I see in your app list) can handle texts and MMS. You can only have one app for texting at a time, and activating another will disable the current one. If you have another app for texts, this one is pseudo disabled, which I'm guessing turns off the notification settings because there's no use for them.
If you are having a notification problem, you should look at the settings of the texting app you actively use. I saw in one of the replies that you are using Google Messenger. I've never looked at out, but my guess is this is the app handling your texts, so that's where I would look for settings.