As a child (when I was interested in bugs) I primarily called them roly polies (that's weird, spelling it out) but also used pill bugs some of the time, or at least I remember hearing both. I think I personally mostly used roly poly.

For what it's worth, apparently "rolie polie" is the de facto standard, if children's TV shows are any kind of authority, or perhaps they just liked the rhyme:
https://www.youtube.com/watch?v=LTkmaE_QWMQ

It's interesting that there's so much variation, but it kind of makes sense: they're all over, harmless, somewhat entertaining for children (when they "roll" up into "pills" ), and there isn't much need to talk about them as adults, so I'm not surprised there are many regional terms!

Also, I think there might be some variation within the species (or several species around the world?), not that a casual speaker would distinguish them. The canonical kind for me is gray.

Awww cochinilla is a cute word!

Yes there must be different species as well - the ones I'm used to in Canada were light grey with translucent edges, sometimes even a bit pinky!  Here in the UK there are much darker, and more round - I have to say I prefer the ones I grew up with, they're quite cute, playing around in the woodpile

Are those things actually wood lice? I've heard that term but didn't know it referred to the same thing. Interesting.

All I really know about them is that they're crustaceans.

When I was a kid, my History teacher told us that Phoenicians who came over to Iberia, sold among other things superb pieces of cloth dyed in a dark red colour (which we call PÚRPURA, a false friend of PURPLE --whose name in Spanish is MORADO) very much appreciated by the King Argantonio and his subjects, of the Iberian Kingdom of Tartessos. The colour was extracted from the COCHINILLA, and I have all my life wondered how on earth this grey bug could give such a brilliant colour.

Well, it can't.

Apparently, there is another species of bugs called COCHINILLA as well; it lives in Lebanon and thereabouts, but has nothing in the world to do with my old COCHINILLA back home. There you are: instead of having many names for it as you have in English, we seem to use the same term to cover two species.

Such is the life of words!