When I turn on my new power inverter all my receptacle show 120 volt from black to ground and 120 volt from white to ground in my rv.Every thing shows normal when plugged into shore power. Any ideals

What does it measure Black to White?

Good Question ma0641, Be careful not to hook up until correct, with the readings you are getting, you may also have reverse polarity. Be sure you have the 120 volts between the hot and neutral, and the hot and ground. Zero between Ground and Neutral.
Has similar symptoms to an open neutral, where the hot will go through a connected load, and returns to a neutral, if open, then you will see the voltage on the neutral.
Is this 120volts only? Plugs or cords may be miswired from factory or other.
Good Luck. May be able to help more if not figured.