So if it is a named character (Vighar, Movarth, Sild the Warlock, Orchendor, etc.) is it safe to store their bodies in your home? On gamefaqs and here I've seen lots of debate, but it doesn't seem like anyone knows for sure.
On a similar note, does it even matter if it is a named character? If I Thrall a Volkihar Vampire, will that also disappear like other generic characters?
Well you're asking the right person.
Certain NPCs just happen to leave behind permanent corpses. There's really very little rhyme or reason to it, sadly - it isn't 'all named NPCs,' or 'all quest-essential NPCs' or anything like that. Let's take Orchendor for example, who happens to have a permanent corpse - in his case his permanence seems to be caused by his dungeon (dwarven ruin, forget the name) never respawning. Since Orchendor is permanent, he'll be that way every time you kill him on other playthroughs. I don't really have a good list of permanents since it's so hard to test for them (more on that in a minute), but I believe Orchendor, Arondil, Sild the Warlock, and Rigel Strong-Arm are among the NPCs who leave behind perma-corpses.
However, in Skyrim moreso than any of its spiritual predecessors in which I've played, it's harder than ever to test for permanency - you've got corpses that refresh after 7 days (pre-patch), 10 days, 30 days; you've got some that are permanent in their respective dungeons but lose it when you take them out, you've got some that are permanent up until a certain vaguely-related quest is completed...it's a friggin' mess, honestly.
So in no small amount of irony, Patch 1.3 makes it easier than ever to test for permanent corpses - simply save, thrall the NPC you want to test, lead them to wherever you want to store them, re-kill them, fast-travel to the furthest walled city from wherever you're at, return, and check - if the corpse is still there, then it's more than likely permanent. Just bear in mind that perma-corpses of named NPCs are still pretty rare, so you'll usually walk away from this scenario empty-handed.
Your other option for permanent corpses post-patch are pre-deads; NPCs you find already-dead in dungeons and whatnot, who are almost always permanent. Of course they're usually low-leveled and are terrible as combatants, but if you want some grim decor in your house, these are the ones to look for.
And if you really happen to be nutty like me, you could just delete the patch and play the game the way it should be - pre-patch, you could keep nearly any corpse in the game around indefinitely provided that you visited the cell you were keeping them in within the refresh window (i.e. never stay away from your house or wherever you're keeping them longer than 7 in-game days).