Looks like a zucchini but you would get a better response if you post this in the "Name that Plant" forum. Post another picture of the whole plant showing its leaves and growth habit. What does it taste like?

It tastes like a more bitter, faint version of a normal slicing cucumber. I also don't think its zucchini, as the zucchini plants I have seen are generally more upright. But I definitely won't rule it out!

I remember once that, in our old garden, one year I decided to grow a couple seeds from a pumpkin we had harvested from it. After that following year’s harvest started coming on, I noticed that, with most of the pumpkin plants, they appeared to be producing normally, but the few I had grown from those home-grown seeds were producing really strange-looking fruit (I can’t really describe it now). We realized that we must have had some “squashkins” on our hands, which would have resulted from the previous year’s squash and pumpkins cross-pollinating and producing those weird crosses.

I wonder if those plants you received, while not necessarily “squahkins”, might be some kind of cross between two different plants, or at least two varieties of the same plant?

It could be a pickling melon. Not sure, though. It doesn't look like a squash to me.

Also, it might be a wax melon of some kind.