Hmm... I wondered at the etymology if Jepang was a loan word from English, as it is closer to the English word Japan than to the Japanese word Nihon. According to Wikipedia though it's actually the other way around, The English word Japan is borrowed from the old Malay word, which is listed as japun or japang. It's amazing how much I learn about English when studying other languages.
It's the reverse, Japan is a loanword, newer than "Jepang".
It would make no sense to "borrow" from English the name of the Japan country.
From Dutch Japan or Portuguese Japão, from Malay Jepang, from Sinitic 日本, likely from an earlier stage of modern Cantonese 日本 (jat6 bun2) or Min Nan 日本 (ji̍t-pún) (in turn from Middle Chinese 日本 (nyit-pwón), potentially from older Old Chinese 日本 (*nit-pˁənʔ) but unattested in Old Chinese-era literature). Compare also Mandarin 日本 (Rìběn), Japanese 日本 (Nihon, Nippon), Korean 일본 (Ilbon), Vietnamese Nhật Bản.
The earliest form of “Japan” in Europe was Marco Polo's Cipangu, the first recorded form in English was in a letter dated February 19, 1565 (published 1577), spelt “Giapan”: Of the Ilande of Giapan, by Luís Fróis (a Portuguese Jesuit missionary in Japan), published in Richard Willes, The History of Travayle in the West and East Indies (London 1577)...
The English "Japan" comes from the Malay-Indo "Japang", not the opposite.
Indonesian people knew about Japan long before European people...
You can see the Japan (in orange) and Indonesia (in green) location on this map. So, why would Indonesia borrows the country name to English??