Hidden files saved by Mac OS X into USB drive
In the normal course of events, I would not expect any information about your Mac to be transferred to a USB drive.
TextEdit can be configured to contain the Author's name in metadata for Rich Text files (.rtf), but not Text files (.txt). See TextEdit's Preferences dialog, or File > Show Properties.
The Finder might save a .DS_Store file to the drive, which would contain data about the folders on the disk.e.g. custom icons, position in windows, etc.
https://en.wikipedia.org/wiki/.DS_Store
No logs or info about your Mac or your username should be copied.