How would you correctly classify say - ECDGAD?
Like, how people will say "E Minor 9th Tuning" or something like that, if you understand what I'm saying - what would you call ECDGAD and how would you classify other tunings?
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Beyond the most common tunings, there isn't a hard and fast classification system. I would just generally call the tuning you give in the question as an "open tuning" as it relates to an open chord. Slide guitarists often use this kind of terminology referring to open C or open G tunings.
In some older guitar music it was customary to give the tuning up front, as no standard was widely accepted across national boundaries.
What may interest you is following the development of the standard tunings, as they may give you some clue as to why we use them and not others. In short, tunings in fifths developed to make playing scales on instruments with short scale lengths easy. Tunings in fourths developed to make playing scales on instruments with long scale lengths easier (imagine a double bass tuned in 5ths... doesn't work.)
Most other tunings are for ease of playing chords, or for the purpose of some very specific traditional music. For instance, American Country musicians recognize a "Nashville tuning" but just about any other guitarist wouldn't know what you are talking about.
There have been literally hundreds of alternate tunings, used to play music on a six string guitar. They are now called "alternate" tunings because there is a commonly accepted "standard" tuning for 6 string guitar that we are all familiar with. So anything that deviates from "standard tuning" is now referred to as an "alternate tuning".
Many of the more commonly used alternate tunings lend themselves to names. Various open tunings are named according to the chord they imply when strummed open - for example Open G, Open E, Open D and so forth. Although there are multiple ways to achieve an open tuning in any key, each yielding a slightly different voicing.
Some tunings such as "Drop D" are very straightforward and the name implies the tuning as does "DADGAD" (often referred to as "Dadgad") and "Double Drop D".
Some such as the "Nashville Tuning" (mentioned by Baordog in his answer) and "Slack Tuning", are just so commonly used in specific applications that they have been given a name that caught on.
Here is a list of over 25 commonly used alternate tunings and the names ascribed to the ones that lend themselves to a descriptive name Alternate Tuning Chart This chart shows how to tune in each of these tunings.
I met an artist named David Wilcox at a house concert a couple of years ago - who claims to have written songs in over 100 different alternate tunings. He made up almost all of them and does not really have names for them but on his website he provides a guide to show the tunings he has used on his published songs. He has even made numerous altered capos with cut outs for different string combinations allowing him to fret notes on both sides of the capo.
Here is a link to a list of some of the different tunings he has used. David Wilcox Alternate Tunings
Some guitars such as the Fender VG Stratocaster powered by Roland COSM technology offer instant alternate tunings at the turn of a knob such as Drop D, Open G, D modal, and Baritone.
Many songwriters I have talked with have told me that they like to experiment with alternate tunings because it keeps them from writing stale melodies and chord progressions that sound like too many of their other songs and inspires imaginative new material because each alternate tuning will inspire different type songs based on the mood or state of mind they evoke.
Whether they have a name that you can pronounce or not, alternate tunings open up a whole new world of possibilities for creating unique and fresh music.
So don't worry so much about naming each alternate tuning. Just keep experimenting and enjoy the process!