I have been unable to decide if I should call it becoming-vegetarian or becoming-vegan. For me, the term would technically mean the same thing: a process of subjectivity that would at the same time be an ethical relationship with other animals. That would mean, at the minimum, that we probably didn't eat their flesh, put them in cages, take away their young, conduct violent and invasive tests, etc. But with that said, which term?
I like the term vegetarian a lot. I like the history of the term, that the vegetarian society claims it comes from the latin for lively. And, originally with the vegetarian society, vegetarian meant pretty much what vegan means today. But, the term vegetarian nowadays has some pretty specific eating criteria. You avoid flesh, but remain okay with eggs and milk. Furthermore, in general it is seen as a non-political term. You seldom meet a vegan whose primary concern is not an ethical relationship to other animals. The same cannot be said for vegetarians.
But my understanding about the history of the term vegan is the people who coined simply took the first and last parts of vegetarian, and they simply made the world because it felt right. Which is fine, but lacks the same sort of wordpoetry that vegetarian conjures up for me.