Thank you for your quick response and for pointing confirming my misunderstanding of what devices you have.
That said, it would be helpful if you filled in a little more detail.
You are "responding to a text" on which device? The watch or the iPhone X? And what sort of notification are you talking about? Reason I ask, is that Notifications can be turned off, or modified only to appear for a few seconds. On the iPhone, this in Settings > Notifications.
From here you can make many choices: When to Show Previews; and Notification Style eg Lock Screen, Notification Centre, Banners and from there choose whether the notification is to be Temporary or Persistent.
You can turn on/off Sounds. And you can make these choices for each separate app on your iPhone X.
And as the X is the means by which these reach the Apple Watch, you have control.
The rest of your post I found a little difficult to understand; sorry.
Ian