The word coinage or formation aka neology is the term being sought here.
The OED defines these as:
NEOLOGY a. The coining or use of new words or phrases; = neologism n.
- figurative. The (deliberate) formation of a new word, etc.; the fabrication of something specious.
1693 Dryden Disc. conc. Satire in tr. Juvenal Satires p. viii
Unnecessary Coynage, as well as unnecessary Revival [of words], runs
into Affectation. 1712 Proposals for printing Treat. Art of
Political Lying 10 Whether the Right of Coinage of Political Lyes be
wholly in the Government. 1787 Gentleman's Mag. Dec. 1081/2
Milton..has enriched our language with some epithets..of his own
coinage. 1818 S. T. Coleridge Gen. Introd. or Treat. on Method
23 in Encycl. Metrop. I The ancients, as well as the moderns, had
their machinery for the extemporaneous coinage of intellect. 1876
E. A. Freeman Hist. Norman Conquest V. xxv. 580 Words of modern
As you can see from the quotes, the usage goes way back. Now, if you
coin a word and you are speaking English, the language of coinage is
English. It really does not matter what your basis for it is. You are
the arbiter. Philosophically, it is a false problem to ask what
language a coined word is "in". It's "in the language" of the coiner.
In short, the coiner is the boss. What freedom!
If you were speaking French, then, the coined word would be French. Though the Académie française doesn't usually approve of it. [in joke]
The word can be formed from anything at all. The "parts" of it do not matter. What matters is the meaning that you, the coiner, ascribe to it.
I was surprised to see that no one mentioned coinage. This is a generic answer which can then be broken down into all sorts of sub-categories.
Here is a blog post that describes this phenomenon. coinage, blending, etc.
"And in some cases, the meaning of these words is broadened. Example, complicated chemical or technical terms (like Aspirin: acetylsalicylic acid) [and medical terms] are adopted as the trademark term and often replace standard terms for e.g. in this example, painkillers." [square brackets, mine].
The author also points out that eponymns are coinages, too. One example: watt from the name of its inventor James Watt.
Many medical words are coinages (some would say blending). For me the undisputed genius here was Lewis Carroll and his nonsense poetry such as The Jabberwocky and The Hunting of the Snark, to name two examples.
Anyone can coin a word but will it stick? Dictionaries are constantly reviewing new words to see if they will be included in the lexicon. They have some rules such as usage over time (such as ten years) and usage in written materials.