Umlauts or trema or diaeresis or ...

Umlauts or trema or diaeresis or just "those two dots over the letter" (of course the words in quotes are emphasized by taking index and middle finger, as in indicating the number two, and punching them toward the person to whom you are explaining what you're talking about).

Officially, on Zoë's birth certificate, she does not have these extra indicatives of how to correctly pronounce her name. Zoë is a Greek word meaning "Life". But, if you were to read it according to the (idiotic!) English language, it would be pronounced like toe, that digit on the end of your foot.

The umlauts (as they are called in German) or trema (which is the actual name for the two little dots) allows what is called a diaeresis, which is where you pronounce the vowel as another syllable and as separate instead of a dipthong (no, not a scary speedo bikini, it's when you slur your vowels- yes, still seemingly sounds in poor taste, but it is necessary when you are calling a train).

According to Wikipedia (the source of all secular knowledge, but that's another post):

The word trema is taken from the Byzantine Greek τρημα, meaning "perforation, orifice". This sign was first used in that language to indicate a phonological diaeresis, that is when two consecutive vowels are pronounced separately as a hiatus, rather than together in a diphthong. It is currently used with this purpose in several languages of western and southern Europe, among them Occitan, Modern Greek, Catalan, Dutch, and Welsh.

For example, according to the spelling rules of Catalan, the digraphs ei and iu are normally read as diphthongs, [ei̯] and [iu̯]. To indicate exceptions to this rule, a diaeresis mark is placed on the second vowel: without the trema the words veïna [bəˈinə] ("neighbour", feminine) and diürn [diˈurn] ("diurnal") would be read [ˈbei̯nə] and [ˈdiu̯rn], respectively.

So, you now ask, since you know why I add the trema to Zoë's name, how do you get these little dots over the E on the computer?

Well, it's easy on the web. There's a shortcut for HTML, and all you have to do is type in ë. Oh wait, let me write it as I am writing it really:
& e u m l ;

It's a little harder on other things. I've got Word set up with a macro so that every time I type Zoë's name, it automatically corrects the e to ë. But, if you want, you can always go in and find the "symbol" to add the umlauts.

At any rate, I like the weirdness, but I try not to get exasperated when people spell her name wrong (drop the tremas, or add a y or subtract the e and add ie, etc.)

Yes, it's crazy how people spell names. I'm included in that group- but only with Zoë's name. I think with my other daughter's I've chosen "standard" spelling (if there is such a thing.)