Does Apple Watch identify "me" while using Apple Pay on Cellular without iPhone nearby? Is it safe to use Apple Pay on Watch like on iPhone?

As far as I know, Apple Watch does not need a passcode or something to pay with Apple Pay nor unlock Apple Watch (but probably it can be set).

Now let's talk about Apple Watch 6 Cellular version in situation when iPhone is not nearby (I left it in home).

As we know, when we want to pay with Apple Pay on iPhone, the phone requires TouchID or FaceID to identify that "we" are we.

Does a similar identification mechanism exist on the Apple Watch? Does Apple Watch know if really "I" am wearing the Watch or when my watch would be stolen, Apple Pay can be used by anybody else as long as then will use it when it is on someone's wrist?

The Apple Watch requires the user to have set a passcode in order to use Apple Pay with the watch.

When you put the watch on, it will request a passcode. You can use Apple Pay only after you have entered the passcode. The Watch by default continuously monitors that it is still on your wrist - if you take it off, it locks itself again and requests the passcode.

You can disable Wrist Detection, but that will disable Apple Pay on the 1st Gen Watch, and on newer watches you'll be prompted for your passcode when you attempt to use Apple Pay.

You can also use the "Unlock with iPhone" feature so that you unlock the Watch with your iPhone (i.e. by entering a passcode on the iPhone or using TouchID/FaceID).