I don't think this is an uncommon problem, but I do think it's uncommon to have a name for it.
I'm significantly time agnosiac. I say agnosiac instead of agnostic because I believe time is a thing, at least for some sense of the word thing. My brain just doesn't register its passing, or lack of passing. Five minutes? Five hours? Five days? Pssht I cannot even tell without a routine, and it's still kind of iffy.
Having no internal sense of time causes two categories of problems: the "oh god oh god I am going to be late/do not have enough time to do this" problem and the "psht whatever I have all the time in the world, oh shit how is it suddenly midnight?" problem.
I have massive, terrible, horrible, awful anxiety about the possibility of being late. It's a panic attack trigger. So I have my routines, I know how long they take, but I round up an hour. Add an hour to any projected times to do things. This means? I am always early. Or almost always early. The busses don't always cooperate. But I am so worried about being late that I am instead ridiculously, obscenely early. This is awkward if showing up at someone's apartment or to meet them for dinner at the restaurant or whatever, but it's better than being late. Anything is better than being late. If I schedule an hour to get ready, an hour for each bus...then I will be on time. I can take a book or crocheting or a notebook for drafting blog posts or schoolwork on the bus and for the wait, at least I am not late.
Not helping this particular anxiety? I was always late as a child because I have too much time urgency whereas my mother figured that on time is for other people. I can't feel time and have always been profoundly aware of that deficit when it effects how a schedule is going to play out.
The other problem with time agnosia is that time just kind of runs away from me. Did I spend an hour, or ten minutes, or six hours doing a thing? Wait, why is it 1 AM? I don't know. Alarms startle me so they're not my first choice. Instead to mark time, I use music:
-I listen to Doctor Horrible's Sing Along Blog to mark chores. It has problematic elements, which I am aware of and dislike. It's the right length & the right level of engaging (not very, songs aren't too difficult to sing with while doing something else) for my purposes.
-I have several CDs or mixes that I listen to while winding down online or doing my schoolwork, so I know that however many hours have passed. If it's on repeat, I am doing it wrong-the purpose is to know when it's been 2 hours, or 90 minutes, or whatever.
-On my ipod I have several playlists that mark how long it takes to get certain places, with the added bonus of shifting my mindset a bit.
Time pieces? Are not as awesome as I thought they'd be. I tried wearing a watch and not only did they keep dying, but I'd also keep checking at what I thought were similar intervals and they...uh...weren't. That did not help the whole "anxious about time" thing. I set my alarm on my phone for one time things and set it on vibrate, and do check my phone for time if there's a reason to, but wearing it on my wrist just makes me more anxious since it seems like such a capricious arbitrary contraption.
Time: it's a mystery. But I cope.