While the Greek meaning of the word Nekro might have been 'of the body', although in searching I find multiple conflicting statements saying it referred specifically to dead bodies, that's neither here or there. Many words in English have changed meaning over time from that of their original root word. If you crack open a modern English dictionary and look through the words starting with Necro- I think you'll find the vast majority, if not ALL of them, deal with death. Necro- means Death in English now. Bio means life but not in they way they are using. Bio means life like plants, animals, and yes humans but they school they propose I do not believe is limited to humans either. The school they call "Life" does not mean what bio means. It is NOT plants and animals, they have a separate Nature school for that it is not about the body it's about positive energy, things like holy, angels, etc. I hesitate to say "Good" because they are trying really hard to separate it from some sort of morality but they have been clear that is it NOT nature which Bio- is and so there is no conflict.
At the end of the day it doesn't even really matter what the root words mean. Most people aren't going to know or care enough to research it. The problem is that Necromancy is a commonly used term in many fantasy and magic oriented games meaning death today. It's going to be familiar to a lot of people and changing what it means is going to be confusing. If you don't believe me just look through these forums as many have already gotten mixed up between the different Death and Necromancy schools... to most they are synonyms. I don't believe many, if any, games at all use the term biomancy so it's not something people are going to be so easily confused about. The fact that it deals with all living things fits the idea of animating bodies, mutating living creatures, healing and harming life.
The school we are talking about renaming, while it includes animating dead bodies, is not about death or corpses specifically. A spell that takes a perfectly healthy living lion and a perfectly healthy living eagle and merges them to create a Griffon would be a spell in this school. Such a spell has nothing to do with death or humanity. It is taking two living creatures and combining them and I believe the name biomancy is very appropriate for this.