Let's rename [ovo-lacto] to [lacto-ovo-vegetarianism].
I noticed that in the tagging prompt to ask a question, typing in
vegetar displayed the option for lacto-vegetarianism but not ovo-lacto. It seems much more likely that somebody is going to start by typing "vegetarian" rather than "ovo". Sure, this could be remedied by modifying one of the tag excerpts to mention ovo-lacto, but why bother when we could just get the name right to start with?
Oh, and I suggest changing the order because Google Trends indicates that "lacto-ovo" is much more common usage, especially in North America.
Yes, the tag is longer but I think that's okay. StackOverflow also ended up moving toward longer tag names over time.