chomp only removes $/, which is a LF (by default). Even on Windows.

That's not a problem because the CR are usually removed by the time you use chomp.

On a Windows build,
text input handles replace CR+LF with just LF.
text output handles replace LF with CR+LF.

Either the OP is reading Windows text on a unix build of perl, or STDIN has been binmoded.

I suppose another possibility is that the input is garbage of the form "name␍␍␊" which is transformed into "name␍␊" on read and chomped to "name␍".