Term for a word that is unintentionally made up of two or more other words?

For example, therapist may be split into the + rapist, neither of which (arguably) has anything to do with the original words.

Another example would be conflagration: con + flag + ration. Or weather: we + at + her.

Note that words like threesome and purebred would not qualify, because the parts are intentional and contribute to the original word's meaning.

It seems to me there might be a word for this, which I would describe as "accidental lexical componentry" — but I'm not sure there is one. And if I do think of one I will be sure to add a supplemental (supple + mental) section (sect + ion) to this question (quest + ion).

Solution 1:

They are called redividers or redivided words:

(puzzles) A sequence of letters that can be segmented into two or more different sentences

2001, David B. Searls, “From Jabberwocky to Genome: Lewis Carroll and Computational Biology”, Journal of Computational Biology, volume 8, number 3, page 344:
Latter-day puzzle makers in a direct lineage from Carroll’s tradition and even more extreme instances of segmentation oddities in what are called redividers (Michaelsen, 1998), for example, observing that the sentence “In every ode linger many” can be resegmented to read “I never yodel in Germany” (Shortz, 1997); such cases serve to point out the duality of the problems of gap assignment and boundary detection, and also inject a combinatorial flavor.

They are apparently also known as charades. Quoting from The Dictionary of Wordplay by Dave Morice:

A few wordplay terms were especially problematic. Recently some writers have tried to upgrade some of the older, more traditional terminology. Some believe that pyramid should be replaced with triangle. Some feel that redivider should replace charade. The terms in the dictionary are usually those that have appeared most often in print. Any other terms may be listed as synonyms, or they may appear as separate entries with a brief notation that cross-references them to the older terms.

There are a number of domain names which have become infamous thanks to their ... redivisibility:

• therapistfinder.com
• penisland.com
• expertsexchange.com
• powergenitalia.com
• whorepresents.com

Solution 2:

The terms pun, false segmentation, and metanalysis are used in discussion of the phenomenon in p. 132 of Attardo's Linguistic Theories of Humor, which cites several other works that might be worth consulting.

Solution 3:

As a humorous neologism, you might call them polyparses.