I normally see finish called out for stainless steel sheet.  ASTM A 480 covers sheet finish for flat rolled stainless and heat resisting steel plate, sheet and strip.  It applies to ASTM A 167, A176, A 240, A 263, A 264, A 265, A 666, A 693, A 793, and A 895.

This not an RA surface finish specification like ASME B 46.1.  Instead, section 11 describes the finish for sheet as follows:
11.1 The types of finish available on sheet products are:
11.1.1 No. 1 Finish—Hot-rolled, annealed, and descaled.
11.1.2 No. 2D Finish—Cold-rolled, dull finish.
11.1.3 No. 2B Finish—Cold-rolled, bright finish.
11.1.3.1 Bright Annealed Finish—A bright cold-rolled finish retained by final annealing in a controlled atmosphere furnace.
11.1.4 No. 3 Finish—Intermediate polished finish, one or both sides.
11.1.5 No. 4 Finish—General purpose polished finish, one or both sides.
11.1.6 No. 6 Finish—Dull satin finish, Tampico brushed, one or both sides.
11.1.7 No. 7 Finish—High luster finish.
11.1.8 No. 8 Finish—Mirror finish.
11.1.9 TR Finish—Cold-worked to obtain specified properties.
NOTE 4—Explanation of Sheet Finishes:
No. 1—Commonly referred to as hot-rolled annealed and pickled or descaled. This is a dull, no reflective finish.
 

fabrication codes may also have requirements for surface roughness.

Here is a link to the surface finishes chart in my website
http://ultra-mat.com/site/products/refractory-metals/molybdenum

You can see the chart on the bottom of the page. It lists the surface finishes in microinches, micrometers and in N-values.

I hope that anyone who is dealing with surface finishes will find the table useful.