There are multiple ways to check for a fake phone.
For some brands, you can just look up the serial number in the manufacturer's site. If the serial isn't found or it says it belongs to a different model, then its a fake.
You can also check that the device info tab in the settings gives you the right information for the device. If the device type(also called model number on some phones) matches what you think your phone is. If it doesn't then theres a high chance that you have a fake.
Also check to see the build quality is what you would expect from the manufacture. Does it look like a new phone is scuffed and its supposed to be from a high quality manufacture? If so then it might be a fake. Check to see it has all the buttons on the side and no extra ones(or missing some).
Finally you can also check the IEMI of the phone. If a quick search doesn't match it up to what you should have, you might not have what you think you have.