I don't know much about the characters, so the second panel made me wonder. Does Nice Nature refers to herself in third person frequently?
She doesn't. She usually uses atashi. (アタシ in katakana, which has a slightly different nuance and sometimes intonation compared to the hiragana variant.)
Though, in the context above, referring to oneself in the third person isn't that unusual. Here it's like making a self-deprecating joke at one's own expense. English speakers do it too, though they will usually add a "here" after their name (e.g. "Johnny here...") or prepend an "old" (e.g. "Ol' Johnny (here)...").
Otherwise, well... appending -san to one own's name is strange.
Really? You don't mind?
If you like it, you can have anotherLunch BoxBut I'm already fullHuh... Trainer is already having lunchWhy do you have two lunch boxes?Ah... Nature-san is in her growth period...Could I have one of those?This is very tasty!