In linguistics, metanalysis is the act of breaking down a word or phrase into segments or meanings not original to it. The term was coined by the linguist Otto Jespersen, from Greek elements meaning "a change of breakdown".
Even more than is the case with folk etymology, for metanalysis to have any interest for linguistics some overt change has to take place. If a speaker of English were simply to decide that alone 'comes apart' as a-lone (like afoot, around, aloft, astern) rather than as al-one (like although, already, altogether), there would be no way of knowing (or caring) that any such novel interpretation had taken place—unless and until something happened, and that something of course is the appearance of the novelty lone (as an attributive adjective. Most adjectives in a- in English are predicate-only, a souvenir of their origin in most cases as prepositional phrases), hence lonely, lonesome and so on.
Historical linguists are divided on whether to consider the creation of a morpheme boundary where none at all existed before to be a special case of metanalysis or something qualitatively different. For example, as analyzing peddlar as an agent noun (hence the creation of the verb to peddle). Some class this as back-formation, but that term is also used for a rather different phenomenon, one involving actual original morpheme boundaries. For example the (very early) replacement of the regular singulars hife and glofe (or glufe) by the forms hive and glove, back-formed from the plurals hives, gloves.
A huge number of English verbs of Latinate origin appear to have been back-formed from nouns in -tion, -sion and the like: profess, relate, pollute, confect and literally hundreds more are, with rare exceptions, first attested a hundred years or more after the first attestations of the nouns profession, pollution, confection and so on. (They hardly could come directly from Latin; formally they often look like a Latin perfect participle, which would be an odd source for a verb.)
Metanalysis across words: an adder was originally a nadder, and an apron a napron, but the initial n was metanalyzed as belonging to the article instead of the noun. Rather more rarely the transfer of the -n- from the article to the noun, as in newt and (obsolete) nuncle (the latter from the respectful term of address mine uncle, and it is well to remember that not long ago a/an shared the alternation with the very common words my/mine, thy/thine). The expression for the nonce is historically for þan āne(s) "for the one time, for the purpose", in which the -n- is what is left of the dative case of the definite article (OE þæm). The phrase at all is commonly pronounced as though the morphemes were a tall.
Metanalysis of words:
Metanalysis of phrases: in the phrase God rest ye merry gentlemen, originally merry was a complement with rest (i.e., "[may God] give you gentlemen a pleasant repose"), now frequently construed as an ordinary adjective modifying gentlemen (and in all probability relexicalized with the current sense of merry, i.e. cheerful, jolly, though that is harder to be certain of). The expression "to rest merry" and the like was once generally current.