I think it would be best to illustrate by examples instead of by words:
- an + other → another → a + nother → a whole nother
- myn + Edward → my Ned
- les enfants /le.zɑ̃.fɑ̃/ (French) → les *zenfants → zenfant (Mauritian Creole)
It can be called ‘Rebracketing’; the linked page also suggests "juncture loss, junctural metanalysis, false splitting, false separation, faulty separation, misdivision, or refactorization."
Your question is closely related to this question, in case it’s useful.