As we are dealing with an Epson 3880 and the way the menus work is totally proprietary to the Epson Stylus Pro printers, so it really doesn't matter what other folks who have Canon or HP printers do.
I print from Photoshop, so while I select "Print" from the menu and want to switch from colour to B&W, the first thing I do is go the menu item that says "Color Handling" and change it from "Photoshop Manages Colors" to "Printer Manages Colors". The printer profile dropdown menu is disabled when you choose this direction, so you can't select the ICC profile for the paper you are printing with. I then go "Print Settings" button and click on that.
This takes me to the Epson print manager and here I will do two things. First of all, I will go to the Color drop box and select "Advanced B&W Photo". The second thing I will do is to select one of the Epson papers that more or less matches the type of paper I am using. As these paper profiles are loaded into the printer's firmware, you do not have access to the ICC profiles from the non-Epsons papers. Profiles are far less important in B&W work than in colour work. However, thickness, drying times, etc. will still impact your print, so if things are not working properly, you might have to tweak the parameters. So you should choose a paper that is similar to the one you will be printing on; glossy, luster, matte, etc.
The 3880 has four black ink cartridges (Photo Black, Matte Black, Light Black and Light Light Black). The Photo Black and Matte Black share the same print head, so only three inks are actually used for a specific ink and you do lose a bit of ink when going from matte to photo papers, as the print head has to be purged. This is one of the reasons you need to select the appropriate paper from the Epson papers as these drive which black cartridge is used.