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theory - Why do we call D# Eb, but also call Db C#?

Eb is much easier than D# from the number of accidentals, and so D# is virtually never used.

Db is more common than C#, but I've seen both. Horn players are usually more comfortable with flat keys and guitar players are more comfortable with sharp keys, so it may just depend on who you're talking to.

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It's all that mess, from wrapping around, at the bottom of the circle. Which one you use is kinda left up to you. Drucifer hit on the head...

Eb is much easier than D# from the number of accidentals, and so D# is virtually never used.

Db is more common than C#, but I've seen both. Horn players are usually more comfortable with flat keys and guitar players are more comfortable with sharp keys, so it may just depend on who you're talking to.

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Seems like we're confounding tuning & key.
Confounding... perhaps. I'd call it more a continuation of an existing convention that applies to all musical instruments using a 12TET tuning system. It works for scales, people understand the enharmonic equivalents, and therefore the same conventions for scales and key are then continued to the instrument's tuning.
 
When referring to tunings, Eb-Standard is quite widely recognized as a half-step down from E-Standard.

However, if we go a step & a half down that's called C#-Standard, why?
It's also Db-Standard, but I've never seen it written out as such.

Well, down tuning by bands with guitars isn't really "theory" and the terminology surrounding such things wasn't really put together by a bunch of music theory experts. It was just what it got called by people who did it. Eb is pretty easy to understand, if the biggest string and the littlest string were an E, if you dropped them by a half step, sure what else are you gonna call it? C#, jeez, who the hell knows? It's not like ANY of it has any kind of logic to it. Or it's the logic of finding the easiest way to fit fingering patterns you know to a different key (kind of like the capo) without having to figure how to actually voice those chords in that key. You don't need to know the notes, you just make the same shape. Yeah, I know, sometimes you need that low E to have more bottom, so tune the shager down. I mean, orchestras do it with 5 string basses or putting a C extension on an existing instrument. Or going the other way and tuning the bass up a whole step (for solo tuning) to extend more into the cello range. But that doesn't change basic music theory and the notes don't change and the construction of chords etc. don't change.

But your supposition that "there is no Cb" etc. is incorrect. There is and it's in the Ab natural minor scale (and others). Ab Bb Cb Db Eb Fb Gb Ab. It looks funny to you because you're used to thinking in terms of frets on an instrument that employs tempered intonation. There's a nice discussion about just and tempered tuning on here somewhere, it's in a head talking about some guitar player's weird frets. So were you to really examine what you were thinking should you be playing and Ab minor scale, it would be along the lines of Ab Bb B Db Eb E Gb Ab. Which would give that scale two 2nds and two 5ths. And since there are instruments in the world other than guitar and bass guitar AND you have to use notes to construct chords with 3rds and 7ths and 5ths and other tensions, 1. if you're going to transpose a line to an instrument (oh like an Eb alto saxophone) you want to be REAL CLEAR about how best to notate that and which "B" you're going to use. and 2. writing out a triad as Ab B Eb is going to cause a lot of confusion since someone is looking for a 3rd degree of the scale, not a 2nd degree. A C E begets Ab Cb Eb etc.
 
I'll tell you why it's also called C#.

My tuba professor at Fred State, (NY,) would seek out F# and C# etudes to torture, err, push my progress with.

One time I thought I had the solution - adjust all the tuning valves to compensate, since he always listened to me with his back turned.
He told me - good - now put the valves back and play it correctly. :D
 
The correct answer is in an early post in this thread:

We choose which enharmonic key to use (b versus # version) based on the fewest number of sharps or flats in the key signature that results from using X named key. At least, that is generally the case, unless there is a special reason not to (which doesn't matter for what we're talking about here).

points of note:
- accidentals are not part of a key signature... sharps and flats are called sharps and flats, they only become accidentals when you have to play a written note that falls outside of the key signature. So if you are in Eb Major, and you want to play an E natural, you have to play an E with the natural sign (the little square thing with a couple stick things LoL... no idea if it's type-able here). That is an accidental, and it only lasts as long as the current measure of music, then is forgotten (on purpose).
- Eb Major has 3 flats.
- D# Major has 5 sharps and 2 DOUBLE sharps. (C## and F##).

Which would you choose to write notation in, discuss with other musicians, and read chords from?

I think it's self explanatory, but we use the key with fewer sharps or flats in it (Remember you can't mix them in a key signature). So Eb Major, in my example, is the best choice.