Okay, here's my take on this.
I see this alot on Ebay. People calling the Axis an Axis EVH, or a Van Halen Axis. Their intentions are to draw the attention of people looking for a Van Halen guitar, although technically that is not what it is. Some people would call this deceptive advertising, but I would disagree.
First of all, if they are not actually trying to charge the price of the collectible EVH model, and they put the word Axis in the ad, it is not deceptive.
Secondly, anybody that is going to buy something that expensive should educate themselves on the product before they buy it.
Lastly, I don't think there is anything wrong with callling an Axis an EVH guitar. Eddie Van Halen designed the guitar shape, and pickup configuration and design. This guitar type did not exist until Eddie and Ernie Ball put it together. There were minor changes to the design when EVH left EBMM, but overall, the guitar is the same. If somone had an original 1984 Kramer Baretta with a Floyd Rose, Maple neck, and hockey stick headstock on E-bay, they would also refer to it as an EVH guitar.
I would say that it is more truthful to call an Axis an EVH guitar than the Kramer, or a Wolfgang for that matter.