Unwritten Rule Of Writing Own Name In mathematics, there is an unwritten rule that one is not supposed to write his or her own name (using initials or "the author" if necessary) or attach his or her own name to something (e.g., to have something named after you, someone else should first call it that).
A few questions:
First, is this rule, in some form, in fact written down somewhere? If so, where?
Second, what circumstances, if any, is it appropriate to use your own name? 
Lastly, does the rule extend to other people referring to the originator of an idea and the idea? For example, is it appropriate to say "X proved the X Theorem."? Or does this make it seem as though (to a small degree) that X broke the unwritten rule? While less explicit, would it be preferred to say "X proved his/her theorem regarding Y on Z."?
I apologize for the "soft" question, but the discussion and answers are certainly appreciated.
 A: I would avoid referring to your theorems by your own name unless they have become completely standardized as such.  This is especially true when you submit a paper establishing a supposed new result since it will likely be considered presumptuous to assume that no one has already proven something similar.  However, it would be awkward not to refer to your name in a theorem if it has become standard terminology.  For instance, when Woodin proves results about Woodin cardinals, what else would he call them?  To answer your second question then, I'd say you should do so when it is pretty much unavoidable not to.  
On the other hand, it is perfectly acceptable to cite your own work, and you should certainly do this.  When doing so however, I would avoid referring to yourself if possible.  Generally, you can do this by saying "as shown in [n]" where n is the (alpha)-number for the article in your list of references.
As for referring to others' work, I think it is generally considered a compliment to name a property or a theorem after the person who introduced it.  However, you need to do your homework first on this, making sure you attribute correctly.  Also, you certainly can say "Name introduced such and such a concept in [citation number]," and this happens very often.  
A: Some additional remarks:
All you said are certainly only unwritten rules, not formal ones; just as there is no written rule or law that one has to be modest or polite. (With the possible exception that some journals might have a specific style regarding certain of these matters; however, if this is so a technical editor will take care of it or you will be made aware of it explicitly.)
I would not say 'X proved the X Theorem' but just as it feels redundant to mention X twice;
but either 'X proved the following theorem' or 'the X theorem' are perfectly fine (in the latter case it should already be common to refer to this result as such or you should be in a position to feel comfortable to suggest naming conventions).
One additional point where I think it can make sense to deviate from the not mentioning the own name in a paper is when it would start to be complicated. What I mean is this, say you write all references in the form Authornames [number]. And the current paper is written by A,B,C who need to quote a paper by A,E,F and another one by C,G,H. Then avoiding the present authors name by saying 'E,F and the first named author [5]' and 'G,H and the third named author [7]' seems sufficiently inconvenient to warrant an exception. 
