As mentioned here, different spellings of names that refer to the same person are not uncommon in Tanach. Deeper, esoteric meanings are associated with the changing of spellings. As a general rule, therefore, you will not find commentators of the p'shat approach that will address these spelling changes.
In this case , the most famous answer is that of the midrash quoted by Rashi:
בחמשה מקומות נכתב מלא ואליהו חסר בחמשה מקומות יעקב נטל אות משמו של אליהו ערבון שיבוא ויבשר גאולת בניו
In five places ["Yaakov"] is written in full form [with a vav] and "Eliyahu" is written in lacking form [without a vav] in five places. Yaakov took a letter from Eliyahu's name as a guarantee that he will come and announce the redemption of his children.
For a more extensive explanation of this midrash, see here