The Artscroll Chasam Sofer offers two answers which addresses the question:
1) Both names Ben-Oni and Binyamin are focused on the concept of strength. Rachel muses that if not for her moral strength (און) whereby she enabled Leah to marry Yaakov that fateful evening, she would not be dying now. Rachel would have been the one married first while Leah, the second of the two sisters married to Yaakov, would have violated the Biblical prohibition of not marrying two sisters. Now however, since Rachel married second she must die upon entering Eretz Yisrael (Chasam Sofer 185)
2) Rachel utilized the Aramaic version of בן אוני- בן צערי which has a double meaning - the son of my suffering, but also my youngest son (knowing she would have no more children). Yaakov, on the other hand, not knowing whether he would merit more children could not call the newborn explicitly בן צערי, my youngest son. He named him Binyamin, similar to בן ימים the son of my days, i.e. my old age. This explains why the Midrash concludes that Yaakov used Hebrew Lashon HaKodesh when naming his son, by contrast to Rachel who used the Aramaic form (Toras Moshe 28a).