My name is also Summer and I have friends in japan. They call me Natsu, summer in japanese obviously, its not a name, no, but they are not confused by it. They have told me it is easier for them to call me Natsu instead of Summer.
Since you are not japanese, you can either go by the name Natsu but it would be worng to introduce yourself as that name (( because you are foreigner )). Your name would be saama in katakana.
Your choice :)
Your choice :)
According to the babel fish translation site the word summer is 夏 in Japanese. The link to the translator is: babelfish.altavista.com