Yes, the brand of the monitor should be eMachines. The OEM of the monitor would be harder to find out. That kind of information is usually not published. Does it matter what is the maker of the monitor though?
Another thing, I looked up the w3400 package that Walmart is offering an it looks like they are selling you obsolete technology. The current entry level desktop packages from the major computer manufacturers (Dell/HP/Gateway-who now owns eMachines) are more powerful than the desktop package you are getting from Walmart. And most of them are cheaper than the listed Walmart price I saw.
If you ordered online direct from the manufacturer then you might find a special. If your credit is decent then you can probably finance it and get your computer within a week (as opposed to layaway.) If your credit is more than decent then you can probably finance it interest free.
Here is your w3400 advertised for $592 This comes with a 17" CRT monitor (soooooo, 20th century

), 2GHz processor, 512 ram, and 80GB HD
Here are Dell's desktops. As you can see the entry level desktop is cheaper and has a better processor and a flat panel. Yes, only it's a 15" but the viewable screen for a 15" LCD is about the same as a 17" CRT. For a little over $100 more you can go up to the next level for slightly better processor and 17" FP.
Here is an eMachine desktop from their website Monitor is sold separately. This desktop plus monitor are still cheaper and more powerful than the Walmart version.
Another way to go is with a refurbished computer. All of these sites offer refurbished computers for sale for even more savings. Sure it's not brand new and someone might have licked it before.

However, if you want to save money then you can get over it.
In fact, a refurb might be more reliable than a "brand new" computer. If a company busts out 1000 computers in a day then they might only quality check 1% of the products. Refurbs on the other hand are 100% QA tested.
Basically, I'm recommending shopping around a bit more with the Dell/HP/Gateways of the world. I hope it isn't too late to take back your layaway.