Mushoku no Tensei – Eris Gaiden

Eris Boreas Greyrat is a former noble girl, who one day was transported to the other side of the world with her cousin Rudeus. She grew as a swordswoman, but ultimately was unable to save Rudy as he was nearly killed. Deciding that she wants to be someone who can support him rather than the other way around, Eris decides to leave Rudeus and go on her own journey.
This is a spinoff of Mushoku Tensei, which splinters off from the main manga at around chapter 51 (volume 6 of the light novel, first season of the anime).