There are two places in halakhah where the criterion for whether something is significantly changed is whether there was a shinui sheim, a change in name. The first is in the laws of Shabbos, something is nolad (“born”, i.e. unusable because it did not exist when Shabbos began) if it underwent a change that changes what we call it. For this reason, one may not melt ice to produce water on Shabbos — “ice” and “water” are different names. (This is true for the few languages I could check. It would be interesting to see if anyone discusses the permissability of melting ice by someone whose first language does not use different words for them.) However, R’ SZ Aurbach is quoted (Shemiras Shabbos Kehilchaso 10:5, fn 15) as limiting this gemara to water. Frozen orange juice is called “frozen orange juice”, and thus there is no shinui sheim.
The second case is in property law. Changing something is a form of qinyan, acquisition of the object. One kind of shinui could be a shinui reshus, moving the object from one person’s property to another. Another is changing the object itself to the extent that there is a shinui sheim. A theif who steals wood and makes a hole in the wood, is obligated to return the wood (and the difference in value). If, however, the owner gave up on reclaiming the object (thus giving up ownership) and the thief made something out of the wood (thus acquiring ownership), the thief would have to repay the value, not return the wood.
This could be understood in terms of applying halakhah to the world as experienced. See (“The Nature of Reality” for an explanation, and other possible cases in “The Unobservable, the Unobserved, and the Observed“.) Word give us labels, but by giving groups of things shared labels, they color our world by defining which set of pigeonholes we use to group things as being essentially the same, and assign new things.
For example, in English speaking countries it’s common to ponder if Judaism is a race or a religion. On the one hand, it is racial in that once someone is born a Jew, they are always a Jew, regardless of belief. On the other hand, someone can join the fold through geirus. But the question isn’t one of Judaism, it’s one of English. These are the kinds of peoplehood we assume exist because these are the words the language gives us. The language was primarily shaped by Christians, though. Therefore there is no guarantee that there exists exactly the right pigeonhole to place Jewish peoplehood.
Returning to the subject of shinui sheim, this is a change defined in human perception terms. We’re saying the minimum unit of change is from one conceptual category to another. The physical magnitude of the change is irrelevant — look back to our contrast between melting ice and melting frozen orange juice. It is measured in terms of change in human conception.