One of the key elements of Isekai anime is that the protagonist remains largely the same person throughout the series, and the story comes from the relatable character from the normal world entering one that is new and unusual. A character may enter that world overpowered or with strange abilities, but the person who is isekai'd is still the same person at the beginning of the series.
Some characters, however, have changes not only to their form but their personality over the course of the series. Physical changes can often appear to be the least significant in this kind of anime and manga, but the changes that occur internally are perhaps both more significant and profound.
5 Sora and Shira - No Game No Life
Protagonist and deuteragonist Sora and Shira are highly intelligent humans who live in an aimless, game-centric world. Considered hikikomori, they have no presence in the real world as anything other than Blank, a mysterious online competitor who destroys the competition. Without purpose, they simply aim to be the best at any particular gaming field and consider real life to be a terrible game.
Transported to Disboard in the land of Elkia, the pair find that the games that they are so passionate about actually serve a genuine purpose. Their lives, while considered meaningless in the real world, instead take on a role of heroic importance. Their lives and their abilities have meaning as they are valued for their skills. They may not change physically, but they grow into the role of rulers that they are presented.
4 Hajime Nagumo - Arifureta: From Commonplace To World's Strongest
Hajime Nagumo is not considered to be well-liked in the real world by anyone besides Kaori, his friend, and class idol, yet he remains kind and caring to others. When his entire class is transported into another world, it appears that even his magical abilities are considered less than impressive and his friendship with Kaori inspires jealousy and attempted murder by a classmate. After being left for dead in the bowels of a terrifying dungeon, Hajime finds the will to survive but comes out a changed man.
Hajime Nagumo faces death and comes to the conclusion that in order to survive, he is determined to only look out for those who he can trust, which no longer includes his classmates. His former personality which is both kind and caring is replaced by a self-serving attitude and an overwhelming desire to return to his home world. Though traces of the kind boy remain, he is changed profoundly by his descent into the dungeon and what he finds there.
3 Rudeus Greyrat - Mushoku Tensei: Jobless Reincarnation
Though a nameless NEET (Not in Education, Employment or Training) in the real world, after their meeting with Truck-kun, they are reborn as Rudeus Greyrat, a boy in another world, and find that they live their life and grow up from a baby. Cursed by the regrets of a poorly lived life in the real world, Rudeus decides to make something of himself in this new world and actually try.
While other isekai protagonists may physically change into monsters or powerful warriors, Rudeus starts as any other human born into this world, except with the knowledge and experience of the 34-year-old man he was in his previous life. Armed with this knowledge, he sets out determined to become someone he can be proud of and finds that through experimentation and by not simply obeying the accepted norms of the world, he can become far more powerful than anyone even considered and possibly even find happiness.
2 Satoru Mikami - That Time I Got Reincarnated As A Slime
37-year-old Satoru Mikami is fatally stabbed and is reborn in another world as a slime. While these creatures are considered weak and simple in this world, his intelligence allows him to transform into a powerful being after absorbing multiple other creatures. After meeting the dragon Veldora, he is renamed as Rimuru Tempest and is set on track to becoming a demon lord.
While the mild-mannered Satoru Mikami never stood out in the real world and was a typical salaryman, Rimuru Tempest is a free spirit and one who finds himself given the responsibility of the lives of an entire nation of non-humans. While the isekai trope is the backdrop for entering this world, the person who was Satoru Mikami is about as different from Rimuru Tempest as possible in both form and psyche.
1 Hiiro Wakaba - So I'm A Spider, So What?
Hiiro Wakaba was a social outcast at her school. Though others saw her as an almost mythical figure, Wakaba did not seem to see it, spending most of her time reading or playing computer games. With her family in a bad state and poor diet, she is often reticent and anti-social, with little interest in her classmates.
Once reincarnated, Hiiro Wakaba finds herself as a spider monster in a labyrinth and is forced to fight every moment of her life. While she may have been distant and uninterested in the world around her, she is now forced to face the reality of possible death every day. While this does not help her to become more vocal with other people, she communicates with the audience regularly, and as they see things from her perspective, they can see this normal, shy girl become Kumoko, the Nightmare of the Great Elroe Labyrinth.