We call it "strutting". I think it varies from chapter to chapter, because I heard some other TX sorors call it "taking it around." Heard "strolling" too.
Motions in the struts vary from chapter to chapter too. Sometimes we'll do something kinda universal (Kick, International) out of town and mannnnn.... pinkys going up while other people rep the region while other people throw mirrors... I guess it's just individual flavor.
As far as jackets, I've never seen one with too much on it except on the internet. I'll be James Brown before I put all
18 of my LS's and our crossing times on my jacket!! But then again, my godmother has one with a huge ivy that covers the entire back and I thought it was a bit much. To each her own, I guess. Chapter, semester, line name and number is more than enough for me.
Also, I have a neo question for sorors - what song do you associate with us? I was wondering if this is regional as well. Down here it's
A Phi A - Pistol Grip Pump
DST - Brick House
Omegas - Atomic Dog
KAPsi - Flashlight
ZPB/PBS/SGRho/Iotas - ???
We have an Ivy Grip strut to "Pistol Grip Pump", but not really a recognized song. I've heard it's "Cutie Pie" by One Way, but we never play that here... I've also heard some song called "Set It Off"....anybody know?

Zetas, Sigmas, SGRhos, Iotas... could you share yours, if you don't mind?
