Retired Honda Power Equipment Guy Here:
All Honda generators are test-fired/run at the factory. For the EU2 series, this is Honda's giant plant in Thailand. They check engine operation and electrical output. It is possible a small bit of fuel remains in the carburetor bowl, so drain it for sure.
Next, Honda recommends a couple of squirts of oil into the cylinder (via spark plug hole). Then, slowly pull the recoil a few times, then stop at TDC when the valves close. If you have already put oil in the engine, it can stay; no need to drain it.
The last time I opened a new one, an EU2 was in a large plastic bag, so use that if you have one or get a suitable one.
Are these the older, EU2000i models, are the newer EU2200i models? Both have a 3-year warranty from the date-of-purchase. It is a good idea to get them both registered with Honda, as this will make any future warranty claim go through smoother, and also provide Honda with a way to contact you in the unlikely event there's ever a product safety recall. Here's a link to register online:
https://powerequipment.honda.com/registration
Finally, when you have the serial numbers for both units handy, check this link for current safety recalls; there have been two for the EU2200i models, one for water intrusion/short circuit and the other for fuel leaking. Use this link to see if you have a unit subject to the recall; if you do, arrange to have it repaired by an authorized Honda dealer at no charge.
https://powerequipment.honda.com/support/recalls-and-updates
Find a Honda Dealer Near You:
https://powerequipment.honda.com/dealer-locator