Look like a buttercup squash ( not butternut)

Definitely of the hubbard family, to which the smaller buttercup also belongs. The shape reminds me of a Jarrahdale, but the latter is more deeply ribbed, Should be a good baking squash in any event!

I just looked at the Ambar Squash from Baker Creek, and it does look similar, though the ambar has even less ribbing than yours, being remarkably smooth. Long ago I stopped worrying about exact varieties of winter squash particularly, because I have found all Cucurbita maxima to be equally excellent. Cucurbita pepo or C. moschata, that's a different story...

"Sweet Meat" is a commonly purchased variety, perhaps a seedling of that.

What was "square" about the plant?

I meant squash. lol