My line's name was "The Pristine Eighteen: The Essence Of Elegance". We picked it because we were amazed that among 18 of us, we were all stereotyped as the "good girls" (thus, pristine, i.e. uncorrupted)
In the past, my chapter has given individual line names that correspond with the total line name.. but when we crossed, our specs just gave us a name appropriate to our experiences in the um.... process. When we take another line, we are allowed to pick our own "big sister" name - does everybody do this?