Were slavs actually the primary sources of slaves for the Byzantines? Is that why they were given the term? Or is it because the words just happen to be similar between the Medieval Greek word for slave (Σκλάβοι, Sklaboi) and the various Slavic language words to describe themselves such as Slovene or Slovenin?
Why did the Koine Greek term for slave change from (δοῦλος , Doulos) to the Medieval Greek term (Σκλάβοι, Sklaboi)?
They dont seem that similar for a mistake to be made, so if it is because they were the primary sources for slaves why do we still use a term in English that refers to them as slaves? Shouldnt it be changed to something like Slovene or Slovenin?
An important thing to keep in mind here is that words are not their histories. While it's true (to my knowledge, at least) that Σκλάβοι and slave derive from Common Slavic slav- or slov-, we should be careful about claiming that this means that a word like English Slav 'really means' "slave". Words can look fairly similar, even identical, and still not have any real or substantial connection as far as a speaker is concerned. For instance, English has two words bank 'financial institution' and bank 'a side of a river'. These two words (unlike Slav and slave) are perfectly identical as far as pronunciation goes. However, there's no apparent relationship between them--any native English speaker would say they're two independent words. This is comparable to the situation with English Slav and slave, the main difference being the historical connection between the forms. I suspect most speakers of English are unaware of that.
As far as I'm aware, not really. Though I am unfamiliar with the term "sklavoi", I've never heard anyone getting offended at being called a Slav. In fact, many Slavs are rather proud of the fact they are Slavic, especially those who consider themselves to be Pan-Slavicists. I think by-and-large, however, Slavs usually go by their ethnicity (ie Polish, Czech, Srbian, etc) rather than the word "Slav".
Slovene and Slovenin just mean Slav; they're simply the Slavic-language equivalents of the word, so I doubt you'd achieve anything by attempting to change it.
TL;DR: Not really, as far as I can see.