Personally I think there are pluses and minuses with being a national or a local. The sorority I belong to is Kappa Gamma Chi. We were founded in 1902 as the Gamma chapter at Emerson College (in Boston, MA). In the 1920's or so the Alpha chapter (founded in 1890) became a part of Chi O and the Beta chapter (we believe became defunct)... so we are now the only chapter of the local Kappa Gamma Chi... Making us Kappa Gamma Chi, Alpha chapter.
Emerson College has about 2,500 or 2,700 students, but we have both local and national sororities and fraternities at our school. Kappa Gamma Chi however was the first sorority founded at Emerson college and we have been local for almost 100 years now and have no intent on going national.
In regard to your question about how you figure out what to name your local, that is an interesting question. I learned there is another local Kappa Gamma Chi in Texas that was founded in 1919.... So I think that there are probably locals out there that have the same name. Hope this helps you out wity your questions!
www.geocities.com/kappagammachi
www.geocities.com/krxalumni