Neither Parker nor Hunter Arms were especially creative either

Parker: The 1899 Catalog lists:
Fine English Twist on Quality T, S, R, P & N (and later as an option on VH guns)
Fine Laminated Steel on Quality I & H
Fine Damascus on Quality G, F, E, & D
Fine Bernard on Quality C
Extra Fine Damascus on Quality B
Finest Damascus on Quality A
See http://www.picturetrail.com/gallery/view?p=999&gid=19025099 for examples.

Post-1892 LC Smith:
F grade hammer gun: English Stub Twist
Quality No. 0 & 1: Good Two Rod Damascus
Quality No. 2, 3, 4 & A1: Good Four Stripe Chain Damascus
Quality No. 3, Pigeon, 4 and A1: Fine Three Rod Damascus
Quality No. 5: Very Fine Damascus,
Monogram: Finest Three Rod Damascus
A2: Choice Three Rod Herring Bone Pattern.
See http://www.picturetrail.com/gallery.fcgi?p=999&gid=17116222

But it really gets complicated with Remington which graded the Damascus barrels on Model 1894 guns as follows:
A Grade: Two stripe Damascus (Boston and Oxford)
B Grade: Three stripe Damascus (Oxford 4 S.J. and Chain J)
C Grade: Finer Damascus (Etoile and Washington)
D Grade: Very fine Damascus (Chine and Legia)
E Grade: Finest Damascus (Peiper and Ohonon)
See http://docs.google.com/View?docid=dfg2hmx7_72xs856hdf

And Lefever also used LOTS of different patterns
http://www.picturetrail.com/sfx/album/view/18020839