This example is specific to when you are using the Canadian English language:
Whenever a zombie or skeleton drops chain boots that they spawned with, they are named "Chainmail Boots". This is written in regular text (or blue if enchanted), to show that the name is the item's default name. However the rest of the chain armour set is named using the convention "Chain <item>" and I'm pretty sure boots should be too.
Furthermore, when you repair the boots with iron ingots / combine with another chain boots / add an enchanted book in the anvil, the name "Chainmail Boots" is automatically put into italics in the way that custom names (and only custom names) are. Alternatively put a non-italics "Chainmail Boots" into the anvil and edit its name to "Chain Boots". The anvil does not give the option to take the item from the right-hand slot with the new name, it just has the red cross through the arrow as if you had not altered the name at all.
These two things suggest the "Chainmail Boots" is correctly named "Chain Boots" in the part of the item data that the anvil checks and only the name that is displayed in the GUI is typoed. (This would explain why anvils think it is named "Chain Boots", and when you repair / combine it the name goes italic because the anvil thinks the name "Chainmail Boots" in the name slot was put there by the player and therefore gives it that custom name, complete with italic font.)
Steps to reproduce:
I noticed this with a couple of skeletons / zombies naturally spawned in my mob XP farm (hard mode) when I was lucky enough to get them to drop some of their chain armour, but I expect it would work if you used spawn eggs until you got a mob wearing chain boots and (with luck) killed it and got the item.
Edit:
Also happens with "Chain Trousers" and "Iron Spade" in English (UK). They do not have to be mob drops - they can also be crafted or spawned with creative. I expect this bug will happen with any item that is called something different to US English in the currently selected language.
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Oh wow, turns out my language had set itself to Canadian English (WHY!?) and the bug fixes itself when you switch back to UK / US English.
Found items doing this in English (UK) language. They do the same glitchy behaviours with anvils. I expect it will be the same with any item that is called something different to the US name in any language; because it is beginning to look like the root cause is anvils check if an item is still its original name using the English (US) name list not the currently selected language.
The inconsistent naming of the Chain-(mail-) stuff in Canadian English can be fixed here: http://crowdin.net/project/minecraft/en-CA (language translation change/add requests are currently not supported on this bug tracker)
Repairing an item in a non US English language does work for me, see screenshot.
Oops, forgot to mention it was multiplayer (sorry). It doesn't happen for me in single player. Do servers have a set language that could be overriding anvils detecting your own language?
Edit: Looking at other anvil bug reports, there are a few also to do with US English being the only language that works fully as intended...
Can reproduce in MP, thus duplicate of MC-1123
Unable to reproduce with an MCEdit-generated zombie. What language do you play on?