jeidsath meant not “tense” but “case.” Only verbs have tenses.
Two stages. (1) In the NT the OT Jacob was distinguished from other Jacobs by keeping his name as Ιακωβ (the transliterated Hebrew form), while contemporary Jacobs were naturalized in their Greek environment with their name declined (Ιακωβ-ος, -ον, etc., 2nd declension), as tends to happen with originally non-Greek names. They’re really the same name, of course.
(2) English translators rendered the one as Jacob but the other as James because by a quite complicated series of linguistic developments the name Ιακωβ(ος) had ended up as James in English. That’s why the King James Version is not the King Jacob Version.