I always see Islam referred to as "Mohammedism" and Muslims referred to as "Mohammedans" or similar terms in older texts. When and why did the shift toward using more directly Arabic terms occur?
I can tell you that it was still in common use in Norway in the 1930s, if the Norwegian atlas published in 1934 that I've got is any indication. On the pages detailing the distribution of major religions, Muslims are listed as "Mohammedans".
Wikipedia claims the term was in use up until the 1960s, after which it began to fall out of favour, but links only a dictionary from 1965 as evidence - and dictionaries change rather more slowly than actual spoken language, as dictionaries take longer to update and go to print. They do quote a paper by Sir Hamilton Gibb from 1969 that states the following:
"Modern Muslims dislike the terms Mohammedan and Mohammedanism, which seem to them to carry the implication of worship of Mohammed, as Christian and Christianity imply the worship of Christ."