I figured out why that wasn't working when I read more precisely the documentation about the SD breakout board from Adafruit :
The SD card library does not support 'long filenames' such as we are used to. Instead, it uses the 8.3 format for file names, so keep file names short! For example IMAGE.JPG is fine, and datalog.txt is fine by "My GPS log file.text" is not!
So I had 10 chars but it only accepts 8 chars in the filename.
Thanks for trying to help me ! :)