Perhaps it was arrogant but the blushing didn't bother him. Women had been blushing over him for years, from childhood friends of Cersei's he'd cared little for to women of the court who seemed to bemoan his status in the Kingsguard and the vows that came with it.
But when she spoke of the fun of serving under a King, Jaime's smile seemed to die on his lips just for a moment. There had been no fun in serving Aerys. Forced to guard a Mad King, listen to his plans and believe there was nothing he could do to change them and then when the old man had finally lost his mind completely make the choice to break his oaths and damn his name forever. To kill his own King. "I don't know that it was fun Lady. But I am Kingsguard for good or ill. I've served two kings and the second would not release me from my vows."
Surrounded by Lannisters, and how Robert had hated it. But Jaime's purpose originally at Cersei's urging was to take the oath so as to be closer to her, and when she'd married the King, just not the one she'd been originally promised to, she'd finally come to Kings Landing. And there it had been happy. There they'd borne three children Jaime could never claim as his.
He'd accepted it of course.
"All the same, I thank you Lady Wellington." he replied, forcing the smile back on his face. He always wore it in situations like this, ones he wasn't in control of. It was a mask, or so someone had said to him once. One he needed. It faltered again though upon her recognition of the name. "Yes I did." he confirmed. "Ser Jaime Lannister, Sworn to the Kingsguard of Robert Baratheon. They have other names for me of course." he said, irritation crossing his features. "But you say my name as if you know of it?"