You’d be surprised how many people don’t know. The simplest way to check your phone's model name and number is to use the phone itself. (Don’t ask Siri - she’s hopeless!)
For an iPhone, go to Settings, and at the very top of the page you’ll see your name and your Apple ID/iCloud/iTunes etc. Tap on it. Scroll down until you see your devices. The first device should be your iPhone; you will see the name of your device, eg: "This iPhone 6sPlus.” Bingo.
For an Android phone, go to the Settings or Options menu, scroll to the bottom of the list, and check 'About phone', 'About' or similar. Both the device name and model number should be listed.