Yes, kind of.
The shampoo ingredients are all organic molecules. This doesn’t mean they’re free-range happy molecules but it instead means that these are molecules – at least conceptually – based on carbon and hydrogen. Carbon, due to it’s very special quantum properties, makes a wealth of compounds greater than the number of compounds of all other elements combined. This literally infite amount of possible compounds needs to be named somehow which is why the [IUPAC nomenclature of organic chemistry](https://en.wikipedia.org/wiki/IUPAC_nomenclature_of_organic_chemistry) was invented.
You guessed correctly that the ridiculous names are assembled from building blocks. However, these building blocks aren’t individual atoms. Instead, they’re common and well-known groups of atoms called functional groups and/or fragments. The names according to the IUPAC system basically are an agreed-upon way of describing which fragments in which order and geometric orientation – at least conceptually – go together to make up the molecules of the substance at hand.
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