- The expected answer seems to be Folk Etymology or a less biased euphemism like Reanalysis, as per Wikipedia
a change in a word or phrase resulting from the replacement of an unfamiliar form by a more familiar one.
- Whether this is the correct answer should depend on context.
- The derivatational process is Back-formation
In etymology, back-formation is the process or result of creating a new word via inflection, typically by removing or substituting actual or supposed affixes from a lexical item, in a way that expands the number of lexemes associated with the corresponding root word
- Back-formation in analytic language is functionally equivalent to etymological reanalysis.
E.g. for "resurrect" to exist "resurrection" had to be reanalyzed as *verb + -ion, or /ʃn̩/ as the case may be, which happened on a wider scale with similar words. Likewise, ham and other words in the same category likely combine with many words, so it looks like a productive pattern. That's analogy when entire paradigms coalesce. This is not really the case here, but it is not a closed class either.
By the time that Cheeseburger was coined, the Hamburger was likely associated with ham for a long time, though it would be a peculiar name when paddies are made from beef. The fact that burger had hitherto no meaning on its own has no bearing, because regular words like bread, loaf or cran as cranberry-morpheme too have no internal derivation to justify their use.
Linguistic relativity is narrower than that. The same holds in principle for ham. We don't have to expect an initial etymology passed on with the condiment, because Hamburg has no monopoly on meat in a bun. To expect users to conform to some lexicographic ideal is the etymological fallacy
Since Mett-Brötchen (cp. minced meat) are popular in northern Germany, and Hamburg's markets are popular for their fresh food, raw ham is a likely ingredient. It's possible that sailors needed conserved meat balls, but there is no obvious significance to the receipt other than perhaps clever small time marketing, which cannot be excluded. Whether in a deliberate pun or by accident, whether from ham ("pork"), hum (a big bite), archaizing ham ("home") ... if the word ham contributed to the proliferation of hamburger as a word, that's certainly notable from a German perspective where ham is otherwise less meaningful. It is not even wrong since the details of its origin are admittedly a bit hazy.
That would make the Hamburg origin story a folk etymology, in my humble opinion, that is, a notable account which is probably, to a certain extend, correct yet inaccurate. The older a folk etymology is, the more likely it is either still uncertain or eventually incorrect. 1. If they are correct they are simply called etymology, or specifically transparent. 2. If the origin is obscure, that's why a folk etymology emerged to stop the gap in the first place. 3. Etymology as an ongoing effort has made advances that turn recent etymologies (1) and long standing riddles (2) obsolete. A particular subset of these is the folk etymology as an object of lexicographical interest. Even if it is obviously wrong, its origin might be informative at the root.
That's why cheeseburger cannot be said to be based on a folk etymology: ham was not replaced with a more familiar ham, its meaning was rather extended one way or another, and it was not replaced with cheese for reasons of familiarity. It's a recent economic coinage.