The word dāsa is an old one. And if you look at a Sanskrit dictionary you’ll see it has a wider range of meanings. It seems to originally refer to some kind of demon. It’s used with senses “demon, enemy, stranger”.
Vedic speakers used for the word to refer to the local inhabitants of India. In this sense it seems to mean something like “barbarian”. Not a compliment in any case.
By time that Pāli is attested (around the 5th century CE, ~a millennium later) dāsa has come to mean “a person of low class” (= śudra), and “servant”, “slave”. It seems perhaps that the distinction between servant and slave was not so clear that they needed two different words. In the caste system of modern India being a member of a servant caste is something that one is born into and has little choice over. So the śudras (who were probably the remnants of the indigenous culture) really were slaves. (Dr Ambedkar believed that the modern Dalit groups were the remnants of Buddhist populations, marginalised by Brahmins because they ate beef - take this with a grain of salt).
Some of the early British translators seem to have been nervous about translating dāsa as “slave” for fear that it might reflect badly on Buddhism (which they were busy promoting as an alternative to Christianity). A term like “bond servant” is simply an old-fashioned euphemism for “slave” (though I see that, unusually, Sujato has perpetuated this anachronism in his translations). Ironically, around this same time, the British East India Company made extensive use of indentured labour (another form of slavery) in India, especially in the opium growing industry. Plus ca change.
It seems that slavery was common: … *Evameva kho, bhikkhave, appakā te sattā ye dāsidāsapaṭiggahaṇā paṭiviratā; atha kho eteva bahutarā sattā ye dāsidāsapaṭiggahaṇā appaṭiviratā …pe…. * (SN 56.87).
Dāsidāsa is a dvandva compound, translated as two words linked by “and”. One need not labour the gender of the slaves. It is simply a quirk of Pāli to constantly over state the case. In English, the word “slave” is not gendered and doesn’t imply only one gender in the way that both dāsa and dāsi do (contrast with “actor” and “actress” for example).
I can’t see how paṭiggahaṇa means “trading”. The word means “acceptance, reception”, “taking”. Dāsidāsapaṭiggahaṇā would seem to mean something like “accepting (the labour of) slaves” or perhaps “accepting (the institution of) slavery”.
All that notwithstanding, dāsa is a common element in Buddhist names. I guess the sense is that knowing what we know, Buddhists are bound to serve the Dhamma?