Honestly? I think you might need to incorporate SOME non-vegan foods into clients' meals at first. 90% of people (even health nuts) have a hard time imagining themselves on a fully vegan diet. I think your best bet might be to include SMALL amounts of (preferably local, grass-fed, organic) meats in plans that are otherwise entirely vegan. When you have convinced people to cut down their meat consumption drastically, it becomes much easier later on to convince them to go fully vegan.
Also you have the convenience of triathlons working well with vegan diets. If you had bodybuilding clients you would have a tougher time getting them vegan.
I think the name can be anything based on 'health' or 'organic' or other words that we often associate with the vegan lifestyle, but that don't necessarily scream I'M VEGAN AND YOU SHOULD BE TOO. Picking a name is tough, and I'm sorry I don't have any good ideas!