To the hyphenation rules are the ones that cause students the most doubts, so it's good to always be up to date studying them to understand the ways in which the hyphen should or should not be used. Even more after the changes with the New Orthographic Agreement that brought changes to some words.
In the case of the word 'well-being' its correct form is spelled with a hyphen, look at the examples:
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Your healthy diet will provide well-being.
Our parents care about our well-being.
O well-being will be guaranteed to everyone.
Its meaning refers to the feeling of security, comfort and tranquility.
And the hyphenation rule tells us that the hyphen should be used in this case, because it is a word composed of juxtaposition, in which two or more words of the language come together to form a new one without its structure being modified.
well + being = well being
This new word is a compound noun, the first word being formed by the adverb 'good' or 'bad', which in this case passes to be treated as a prefix, and the second must be a word beginning with a vowel or the letter 'h', as is also the case with:
good-humored/bad-humored, well-being/discomfort.
In the case of ‘bem’, even if followed by another consonant, even if it is not the letter ‘h’, the hyphen is still used, as each of the words in juxtaposition assume independent meanings.
welcome, welcome, welcome
Unlike the case of 'evil', in which the two words must be joined to create a new
ill-bred, ill-begotten, ill-behaved
