Many fraternities use a different naming convention for alumni chapters from undergrad chapters. While nothing is stopping you from having your Beta chapter happen to be an alumni chapter, I would advise against it.
Some fraternities name their alumni chapters after the cities in which they are chartered. Others would use a Greek letter at the end to mean "alumni" for that organization. In Alpha Phi Alpha, the Greek letter Lambda denotes that it's an alumni chapter. You will want to choose what works best for you.
As you decide on what to name it, you will want to develop guidelines for what makes an alumni chapter different from a collegiate chapter.
Thinks to consider (you don't have to answer these questions here):
1) Will alumni chapters have the ability to confer membership or will they just be for people who crossed in undergrad?
2) Will the alumni chapter have to implement a program of service that is identical to collegians, or less time consuming?
3) What will dues be? Where will the dues go?
4) Do you want to plan a national structure first?
5) Will this structure include men for whom their only responsibility is setting up chapters? Note that not every active alumni member will want to (or be good at) expansion -- separate the duties of an active alumni member from that of a VOLUNTEER or elected person.
Hope that made sense, I'm sleepy