Well… common names seem to originate in two main ways.
Older common names were generally used for these plants before they had scientific names applied, or at least they were used by people (e.g. farmers, gatherers) who didn’t have any need to use the scientific name. For that reason, they’re often “misaligned” with scientific names, so a particular taxon may have different common names in different regions and cultures, and a single common name may apply to a bunch of different species, sometimes not closely related ones. In these cases, determining why a plant has a particular common name often is a matter of conjecture.
In contrast, a newer common names may be proposed by the scientist describing particular new species. Or it may have been coined by a naturalist who preferred to use a non-Latin name. For those reasons, many newer common names are direct translations from the scientific name and are specific to that taxon.
“Spanish Clover” seems to be one of those older cases where several different plants have been given the same common name. Several of these plants have also been called “Mexican Clover”. And most of these plants also have other common names.
- Acmispon americanus, your plant
- Desmodium incanum, a Ticktrefoil or Tick Clover
- Grona heterophylla, another Ticktrefoil
- Medicago sativa, more commonly known as Alfalfa or Lucerne
- Richardia scabra (see this reference from 1879)
- Trifolium pratense, an actual clover
It looks like Acmispon americanus received its initial scientific description in 1812 as Lotus sericeus, and spent a long while under the names Hosackia purshiana and Lotus americanus. I can’t find any 19th-century references to Spanish Clover as a common name for this plant, but it does show up in the 1902 Botanical Survey of San Jacinto Mountain.
That 1902 source doesn’t give any suggestion as to the origin of the common name. The OUP has a blog post from 2016 on the etymology of “clover”, which is best summarized as being uncertain. The writer feels that most likely the word comes from the same route as “cleave”, in the “cleave to” sense of being adhesive and may refer to the sticky sweetness of Trifolium sap. Regardless of the origin, “clover” seems to have become used very widely for many related plants in Faboideae, especially if they were used for animal forage or found in meadows.
I would guess that the “Spanish” element came from an association with Spanish-speaking (i.e. Mexican) ranchers in either California or Texas. I can imagine various native Faboideae plants that were palatable to cattle getting called “Trébol” and then “Spanish Clover”. Absent a citation that explicitly gives an explanation for “Spanish Clover” I think that’s probably as close as we’re going to get.