To summarize, well requires a hyphen when it functions as part of a compound adjective (generally when it precedes a noun). There is no hyphen when well functions as an adverb (usually following the noun being modified and a linking verb, such as to be), or when it is qualified (as in extremely well groomed).

Does well organized have a hyphen?

Use a hyphen with compound adjectives when they precede a noun. When the description follows the noun, no hyphen is necessary. The party was well organized. ... Do not use a hyphen between an -ly adverb and an adjective or after an adjective in its comparative (-er) or superlative (-est) form.

Do you hyphenate well defined?

Each attribute in a DICOM Information Object Definition has a well-defined meaning..." It is one of those compound adjectives that are hyphenated even when they are placed after the verb "is" or similar verbs.