How can I verify Apple Watch Ultra 2 serial number is real

I presume you're worried that this is a fake. Is this an Apple Watch you have in your possession or otherwise have physical access to? If not, and you're getting the serial number from seller's website or otherwise being given it, then checking the serial number won't be of any benefit since scammers can post any serial number they like, including one from a different Apple Watch which they may or may not have.

If this is a Watch you can examine yourself, you can check the serial number through Apple's warranty coverage site:

Check Your Service and Support Coverage - Apple Support

While not an absolute guarantee, it's at least a step to confirming that it's a real Apple Watch. For other tips, see:

https://www.igeeksblog.com/apple-watch-original-or-fake/

If you're considering buying an Apple Watch from someplace other than Apple or an authorized Apple reseller, I're recommend reading this:

The All Too Common SAD Reality of Buying … - Apple Community

While mostly aimed at the iPhone, it largely applies to any Apple device.

Regards.

No verification needed. If you bought the watch from anyone or anywhere than Apple or an Apple Authorized reseller that watch is likely A) Stolen or B) counterfeit.

I assume you are asking about this because you bought the watch from a questionable source?