[From the name, she's assuming he's Japanese, and that doesn't sound like a last name to her... and she's certainly not familiar enough with him to want to call him by his first name.]
My name is Pekoyama Peko. I am the Super High School Level Swordswoman.
[So... according to her, there isn't much more to her than the sword. Also she says 'Super High School Level' as if it's completely normal and not at all a weird title to have to rattle off.]
no subject
[From the name, she's assuming he's Japanese, and that doesn't sound like a last name to her... and she's certainly not familiar enough with him to want to call him by his first name.]
My name is Pekoyama Peko. I am the Super High School Level Swordswoman.
[So... according to her, there isn't much more to her than the sword. Also she says 'Super High School Level' as if it's completely normal and not at all a weird title to have to rattle off.]