First, make sure you have "line" as the forward indicator in the Color palette. If not you need to click on the line indicator side of the fill/line controller in the upper left of the dialog.
Secondly, once the Color palette is properly setup Illustrator should display the line type name just below the color slider. However, the name will only appear if you have _only_ one type of line selected.
For example, if you have only crease lines selected the word Crease should appear below the slider. However, if you have a crease line and a cut line selected simultaneously the line indicator in the left side will show little question marks (?) in the corners of the controller.