Just tying a few knots from what has already been suggested:

This sounds like the name of an Inn, except Aes Sedai would frown on an Inn with a name like this, and in Caemlyn especially a sign like this wouldn't stay up long. Aes Sedai wouldn't appreciate a reference to an Accepted, and would be angry with the confusion some might make with the Amyrlin Seat. In support of this, such a thing was mentionned in New Spring, about a new Inn named The White Tower.

So, if this is an Inn, it's probably a new one.

What "funny" story about a "seven stripped lass" in Andor could inspire someone to give this name to his new Inn?

Well... obviously the stories that must have reached the streets by now (especially since those who met the "seven-stripped lass" are now back in the city of "the girl who was made Amyrlin Seat": Egwene).

So, that's a new Inn named after Egwene and Mat ends up there, and has a good if astonished laugh at the sign... how fitting - that fool girl is now so famous she has Inns in Caemlyn named after her... Joline and company will have fits over it, Mat will defend the owner: "well, you AS did put a lass on the Seat, didn't you?" "Well, Master Cauthon, some might also say some fool soldiers also made a boy their general..." *cough*

But is that a "new" Inn, really? I don't think so. My best shot is that (as been suggested) Mat and Thom went to the Queen's Blessing to meet his good friend Gill (or stay there), and found out that with the prolonged absence of Gill, Cook had no choice but to sell the Inn, which has been renamed by the new owner "The Seven-stripped Lass" in reference to the big joke in the city that the Aes Sedai have put a mere Accepted on the Amyrlin Seat - which obviously can't be real, so there's no harm in that name, is it?

That would fit the first Mat chapter: he is newly arrived to the city, Thom and him went to the Queen's Blessing, it's been renamed, and they are brought up to date by the new owner about Elayne being Queen (perhaps already crowned) - and Mat makes some wisecrack to himself about the Inn name being, alas, not a joke.

Naming an Inn after Egwene's story would be a very Jordan-like joke and continue a trend/joke... Egwene has moved from the Winespring Inn to get raised Amyrlin... in an old Inn in Salidar (the so-called "Little Tower" and recently got to play the Inn serving wench to Elaida. This would also mirror Rand, who is starting to get Inns (one in Tear) named after him.

This would also continue the joke of Aes Sedai references (or presence) seeming to pursue Mat wherever he goes...