Nagi

Nagi (ナギ) is one of the main characters in Eve no Jikan.

She is the manager and possible owner (see below for details on her hypothetical background) of the titular coffee shop.

She is one of only a few individuals in her society who see androids without prejudice or mistrust and runs her cafe with one simple rule in mind; do not discriminate between human and android patrons.

Her cafe is a grey zone for those who wish to assimilate with others of a different nature and androids freely deactivate their holographic rings to blend in when present.

She even goes so far as to treat an antique robot who is clearly artificial, named Katoran, as if he were a human customer, regardless of his poor social skills and inability to understand why people go to coffee shops or socialize.

She is one of the most compassionate characters in the series, as she pounces upon Katoran with a hug to make him feel loved and wanted in his last moments before deactivation.

Possible Origins
Her origins and motivations are shrouded in mystery, although the credits and post-credits of the film edit provide some clues.

According to these, and also one of the last scenes of the film, she is the survivor (possibly sole survivor) of a shadowy incident that left others dead. The CEO of a robotics manufacturer resigned after this incident, so it may be that an android malfunctioned. This is supported by the stills shown during the credits where a young Nagi and a robot are seen both injured and unconscious on the ground, then she is seen in hospital on life support with a stranger overlooking her.

This man then brings her home from the hospital, indicating it may be a relative. The then set up various cafes, but close due to the mans arguments with an unnamed woman in the credits. She looks a lot like Dr. Ashimori.

In the closing epilogue, Nagi returns from the cafe and greets the man who has a robotic arm and a robotic synthesized voice, and he asks if the people there are doing well and if the cafe is working out. He then says that he is "anxious since Ashimori broke her" and that this is the 3rd or 4th time they have had to move residence and set up a new cafe. Whilst we do not know who this "her" is, it is probable that the woman in the credits is indeed Ashimori and that this man is the often referred to Shiotsuki, a prominent figure in the development of androids, and that they fell out over the purpose of androids and their role in society. Attempting to leave Ashimori and begin helping android integrate, he and Nagi now set up establishments that act as sanctuaries to facilitate this. We also know he is a skilled programmer as he is seen working on his computer in the final scene and is seen designing the electronic sign that is present at the entrance of the cafe.

The above is only conjecture, but it is indicated that Nagi and the man are both connected to the incident 10 years ago, and that they have both taken it as their mission to help androids and humans coexist.

It is also shown that Nagi has a very subtle version of the man's arm, clearly a more advanced replacement of her own arm from the accident 10 years prior. This is perhaps motivation for her running the cafe, as she may feel like she is part android herself.