It didn't exactly go from Jacob to James. It went from Hebrew (Yaacov) to Greek (Iakovos) to Latin (Iacobus). Latin has no K, so it transcribes into C. The last O traditionally became U in Latin. Also the Greek V is written B (but pronounced V). There is no Latin B in Greek. To write it, Greeks write MP and empirically pronounce it mp, mb or b. Let's break the Latin B into Greek style MP=Iacompus. The Romans did not like to pronounce the letter I with another vowel such as A, E or O at the beginning of a word. They changed it to J which they pronounced as Y (as in Yesterday). Josephus the historian is the Hebrew name Joseph (Hebrew Yosef, Greek Iosif) Even the name Jesus follows this practice. Hebrew Yehsua, Greek Iisus. Justus, Jared and a host of other names all follow the same pattern.
So we have Iacompus=Jacompus. Dropping a letter in a word is common practice in most languages. For example, we write ChrisTmas but pronounce Chrismas for easier reading. For speed reading of a foreign word, Jacompus, the p had to go. And it did. Try it and you will understand why. The French took the name, and because they stress their words on the last syllable, they had a problem with this. They had to shorten it, so they turned it into James. Half of the English language is nothing but French words. James was taken into English, and that answers your question.
Just remember that in Jesus day most Jews also had an equivalent name in Latin and in Greek because of the Roman Empire and the widespread Greek Alexandrine language (or Koini Greek) everybody spoke. It was an adaptation of their own name or an entirely new or second name. Matthew and John were originally Hebrew names. The Gospel writer Mark was also called John. The Jewish apostles Philip and Andrew evidently only had Greek names.