I believe the Today/Upcoming/Later groupings in My Tasks are officially known as ‘priorities’ but I think of them as ‘Planned Start’.
Why is it that these don’t also show within the tasks themselves?
Would it not be easier and convenient to have every task show a Planned Start and be able to change them there too?
I would also like to be able to edit these names and add custom ones (eg “AM”, “PM”, “This Evening”, “Tomorrow”.
They do, actually, though it’s pretty subtle. There is an icon that displays in the Assignee area when a task is set to Today, Upcoming, or Later:
The icon that displays matches the icon that shows in the right-hand column of the My Tasks list. (The one in my example above is the “Later” icon.)
Wow, that IS pretty subtle, especially at my screen resolution!
Do modern developers have to pay rent per pixel usage? 
Thanks for pointing this out
It doesn’t look like you can make a change from there though?
Yeah and you know, Asana’s HQ is in San Francisco where the rent per square pixel is especially high.
No, you can’t, for some reason.
@Alex_Bailey1 and @Phil_Seeman,
Actually, it is possible to adjust the Marked For value even when not in My Tasks:
Larry
Ah, right, thanks, Larry - I forgot about the keyboard shortcuts!
@lpb, thanks for sharing that ‘hidden’ feature! 
I see that the selection jumps down to the next task on the list after using one of these shortcuts.
I guess that’s to speed up processing tasks as a batch. You just have to trust its made the change or click back to the previous task to check.