In S1E10, Emily un-invites Lorelai to her Christmas party, but asks that Rory come alone. Rory asks if she should put Lorelai’s name on Emily’s gift, and Lorelai responds, “Yes. Sign it ‘The Innkeeper formerly known as her daughter.'”
This is most likely a reference to the musician Prince, who changed his name in 1993 to a symbol, forcing people to refer to him as “The Artist formerly known as Prince.” The name change was likely motivated by ongoing contractual disputes, which is strangely fitting for Lorelai and Emily’s situation as well.