SUZGOODNIGHT, thanks for confirming what messaging app you were using. Ann154 is correct we want to make sure your Verizon Messages (Message+) app is the default messaging app. To check that this is the case, you'll use these instructions: https://www.verizonwireless.com/support/knowledge-base-216719/
Make sure VZ Messages/Message+ is the default messaging app. Once that's done, see if one of your contacts can send you a text. This will test and let us know if that double notification occurs. Let us know what you find.
Follow us on TWITTER @VZWSupport
If my response answered your question please click the _Correct Answer_ button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!!