> Does Forth really reduce the burden of naming things?

I would say that you have less names, but they are more important. Plus, it is more difficult to name things because you prefer short names; in all languages, when you have a good naming "discipline", follow a naming convention, you end up with an informal "grammar" inside of your names. In Forth this is even more important.

> My impression is that there's more words in a Forth program than functions in an equivalent program in a language that has named variables

Yes, some people have called that "ravioli code" or "confetti code", IIRC. But most of them are support words. In Forth, you also eventually end up with "module APIs". This also exists in C or Java or ..., except the ratio useful:support is lower.