Regarding the name, Eira is a Japanese female name, but the weird part about it in this case was that it's written in katakana as if it's foreign. That's difficult to convey in Roman script without a very obnoxious translation note, especially since we're not actually 100% sure about what the exact intention here was (outside of the capoeira pun). Unfortunately the translation, even though it's fairly straight, gives the impression it's a Brazilian name.
Either way, all Rentarou does is bring attention to it as if he can see it's spelled unusually. Basically, as far as I can tell, the name is Japanese but looks foreign, hence why she explains she's Japanese-Brazilian.
