This condition is named for John Langdon Down, the English physician who first published a work about the syndrome in 1866. (He didn't suffer from it himself, which is why it's usually spelled "Down syndrome" in the United States.)
Dr. Down was a superintendent for an asylum for children with mental retardation, and he noticed that several of the children there shared a common set of physical features -- most notably narrower-than-normal eyes, leading to his choice of the term "Mongoloid" to describe them as a group. Asian researchers began pressing for that word to be dropped in the 1960s, and "Down/Down's syndrome" was used instead.
Keep in mind that scientists like Down also used the words "idiot," "imbecile" and "cretin" in a wholly factual way. To put all those words in context, here is an excerpt from Down's first paper on these children, "Observations on an Ethnic Classification of Idiots" -- which wasn't meant as a medical paper at all, but a scientific approach to the question whether race rigidly divides the human species:
The great Mongolian family has numerous representatives, and it is to this division, I wish, in this paper, to call special attention. A very large number of congenital idiots are typical Mongols. So marked is this, that when placed side by side, it is difficult to believe that the specimens compared are not children of the same parents.....
The hair is not black, as in the real Mongol, but of a brownish colour, straight and scanty. The face is flat and broad, and destitute of prominence. The cheeks are roundish, and extended laterally. The eyes are obliquely placed, and the internal canthi more than normally distant from one another. The palpebral fissure is very narrow. The forehead is wrinkled transversely from the constant assistance which the levatores palpebrarum derive from the occipito-frontalis muscle in the opening of the eyes. The lips are large and thick with transverse fissures. The tongue is long, thick, and is much roughened. The nose is small. The skin has a slight dirty yellowish tinge, and is deficient in elasticity, giving the appearance of being too large for the body....
They have considerable power of imitation, even bordering on being mimics. They are humorous, and a lively sense of the ridiculous often colours their mimicry. This faculty of imitation may be cultivated to a very great extent, and a practical direction given to the results obtained. They are usually able to speak; the speech is thick and indistinct, but may be improved very greatly by a well-directed scheme of tongue gymnastics. The co-ordinating faculty is abnormal, but not so defective that it cannot be greatly strengthened. By systematic training, considerable manipulative power may be obtained....
If these great racial divisions are fixed and definite, how comes it that disease is able to break down the barrier, and to simulate so closely the features of the members of another division. I cannot but think that the observations which I have recorded, are indications that the differences in the races are not specific but variable.
These examples of the result of degeneracy among mankind, appear to me to furnish some arguments in favour of the unity of the human species.
As more and more came to be understood about the role of genes and chromosomes in the 20th century, scientists began to speculate that Down's syndrome was chromosomal in nature. This was confirmed in 1959 independently by Jerome Lejeune and Patricia Jacobs, who identified a third copy of the 21st chromosome as the cause and introducing another name for the syndrome, trisomy 21.