This old English word means “people”, apparently.

The -scype part is directly analogous to -ship.

What is the þeod part connected to? Know of any relations?

It’s got many Germanic cognates (including deutsch), which you can see here; the Germanic root is in turn from this Indo-European one.

Very interesting!

When I saw Old High German diet I thought it might be connected to the word meaning assembly, but of course that’s from Latin, isn’t it.

[edit] fixed typo

Fits in with ancient Gothic names like Theoderic, Theodahad, Theobald, etc.

Perhaps its most commonly found in the Old English theoden, meaning “king, prince;” a literal translation might be something like “people’s leader.” And yes, Tolkien took the name of the character from this word. All the examples of Rohirric language in LOTR are actually just straight up Old English.

And, I believe, geþeode means language.