If I am seeking lumber that has an actual thickness of 11/16", what nominal size (e.g. nominal for 3/4" actual is 1x...) should I be looking for? I need it for a window trim.
"1 inch" with an additional trip through the planer - ie, it's not stock. For that matter, what is "stock" for various sizes varies with vendor, over time, etc. - the place I used to get hardwood in central NY planed 4/4 to 13/16" unless you asked for a different thickness, so 3/4 would not be "stock" there.
With rare exceptions any lumber thinner than 1 inch is made by planing from 1 inch (actually "4/4 rough") in practice. A well equipped lumberyard (not home cheapo) can custom-plane it for a nominal fee, otherwise you are going to need access to a planer to get this size.
There is trim out there already milled to 11/16", but you will need to rip one edge or another of to get square stock if that is what you are looking for. The first I found was WM 412, it will need both edges ripped and redressed. There is another that is a window sill that will only need one edge ripped off, WM 1021. These are just examples of profiles, some may be finger joint, some may be MDF or what have you, but the idea is there is a trim out there that is the right thing you need if you don't mind a little extra cut here or there. As a note, these numbers I gave are for one supplier. I believe other suppliers use their own numbers to designate their stock. There may be some similarities, Some numbers may be the same as in the 412, but the letters change for the different supplier.