Best person to come up with some ideas is you. ^^
The following questions may help. However, I am not a ls owner so what do I know?
1. Why do you want to make an ls? Do you want to make it because it's the popular thing to do? Or because you want your group of friends to communicate with eachother without having to be in a party or playing /tell tag?
2. What theme is your ls? Do you want the ls to be a badge of identity? TheGalkanArmy sounds pretty good if you want the theme of your alla name to go in FFXI. Or maybe HulcksPosse or something. Do you want it to stand for something you believe in? Like TheHelpfulLords would be a nice ls where people would help all newbies learn the ins and outs of the beginner levels and the first level they start to party.
3. Organization. Will you have a structured ls where certain people of rank (your trusted friends, let's say) can be pearlsack holders and recruit people according to criteria you create? Will you be the sole giver of pearls? This is an important decision because you don't want your ls to grow too big too fast, nor do you want it to just be 5 people. Unless that's exactly what you want to do.
4. Reasons why people should join your ls. This is important. If you just want a handful of friends, then no sweat. But if you expect your ls to grow, you have to give them a reason to join--a reason to accept your pearl and have it take one slot of their inventory. Not to mention bother to equip it. If you want an helper ls, then that may be reason enough. Otherwise, you will have to take time outside of gameplay to plan events. Chocobo races, Garrison events, scavenger hunts, etc.
Never underestimate the responsibility of you being an ls owner. If you can provide ways to keep your members enjoying themselves or at least give reason to equip your pearl, then your ls will be successful.
Good luck in your endeavour!