How to setup Unlocked Phone on other network?

I bought a new Unlocked Note 4 and a Verizon Month to Month Plan. It comes up on Verizon just fine.
To test the phone inserted an ATT SIM from another phone. Talk and Text on the new phone number worked just fine. Can switch SIMs at will and the Note 4 will work Talk and Text just fine.
But, no internet connection. Can not access the web.

Is there some other setting I need to find and change? The phone is not actually unlocked and I should return it?

Thanks

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