Kara tried not to laugh. The truth of it was that there was no humurous intent behind it. The two young men weren't, in so far as she could tell, trying to be funny. Blood in particular seemed rather uncomfortable and unprepared for the whole thing. Her cousin had been the world's greatest hero. Her cousin fought valiantly, and her cousin fought well. Her cousin still died. Kinda. Yet Kara could still so no reason to be so uncomfortable by the death or the act of grieving. Kara celebrated Kal-El. Stupid name and all, his life and achievements were as brief as they were extraordinary. Making it uncomfortable seemed the height of comedic irony to a Kryptonian girl. 

Humans were weird. That thought alone had festered, as had a few other thoughts on humanity, since her arrival. Then Roy misstepped? At least he seemed to act like he had. The facepalm was dramatic and instant, and at least the sight of it made her pale pink glittered and glossed lips curve at the corner slowly turning into a smile. Especially given the truth of the name. One truth she was more than happy to share with this red themed human. 

"Superman? It's not ours. That shield isn't an 'S'--it's a symbol. It's the sigil of House El, a very old Kryptonian bloodline, the one in which Superman belonged to and the one I belong to. My decision to go with Supergirl was convenience. Everyone on this planet knew what the sigil of House El meant to them. It meant Superman. Brand recognition like that it would've done more to confuse if I had called myself anything else. Nightwing? That's Kryptonian."

Then she muttered. Something about why an Earth hero would want a Kryptonian name and "hew-mans" being beyond her.