The only component of Command is a verbal component. From the spellcasting rules on verbal components:
Most spells require the chanting of mystic words.
From the Command spell:
You speak a one-word command to a creature you can see within range.
So the question is whether the spell requires verbal spellcasting in addition to the one-word command. If it does, it would be obvious that you had cast a spell. If one word is all that is required, a surrender request could appear entirely non-magical.
Given that the casting time of Command is an action rather than a bonus action, I would assume that it requires more than just a single word. Contrast with Healing Word and the spells in the same line, which only use a bonus action, and it seems clear that there is more than a single word involved.
According to Jeremy Crawford, the one-sentence verbal suggestion used when casting Suggestion is not the verbal component, and I would assume similar logic would apply to Command.
Yes, wizards need to prepare spells multiple times to cast them multiple times.
From the page you have linked:
(If you've prepared multiple copies of a single spell, you can cast each copy once.)
Think of it this way: When a wizard prepares a spell, it's like he's loading a bullet into the chamber of a gun. The bullet is the spell, and the gun is his mind. He can load silver bullets, or fire bullets, or steel bullets, or whatever other kinds of bullets he has. He can fire the bullets in his gun in any order, but he needs to load two silver bullets if he wants to fire two silver bullets later.
It's the same with spells. You have to prepare a specific spell in a specific slot, and once you cast the spell in a particular slot, that spell can't be cast again unless you have it prepared in a different slot.
In one of the D&D 3.5 books (I think it was the Player's Handbook, but I may be wrong), there was some flavour text explaining how this worked in-world. Basically, each spell was cast in two parts; a long part and a short part. The long part was cast while preparing spells. This part requires more time and concentration, and once completed, you had a partially-finished spell hanging around until you finished casting it. The short part is what you do to cast the spell mechanically. For example, the standard action used to cast fireball would be the short part of that spell. The idea was that a wizard had to cast the longer part of each spell beforehand, and could only have a limited number of partially-cast spells hanging around at a time. Since casting a spell uses up the prepared part, casting multiple copies of a spell in a day requires preparing the spell multiple times.
If you really don't like this rule, it can be houseruled out pretty easily. A version that I've had some success with is to have wizards prepare a smaller number of spells than usual, but to allow them to cast those spells spontaneously. The way I would run it is as follows:
For each spell level other than 0, wizards can prepare a number of
spells equal to their normal number of spells per day, minus 1,
minimum 1. The number of spells that can be prepared does not take
into account a high intelligence bonus. For example, a 9th level
wizard can prepare 1 5th level spell, 1 4th level spell, 2 3rd level
spells, 3 2nd level spells, and 3 1st level spells. Wizards can, once
per day, spend 15 minutes meditating and studying their spellbook to
change out 1 prepared spell per level. The number of spells that they
can cast is unaffected. Wizards can cast any spell that they have
prepared any number of times, subject to their spells per day limits.
This does not count as spontaneous spellcasting for the purposes of
metamagic feats, or other features that provide benefits to
spontaneous spellcasters. If a wizard wants to cast a metamagic
version of a spell, the spell must be prepared that way.
My experience with this ruleset makes me believe that it's pretty fair. The wizard loses a bit of it's minute-to-minute versatility, since they can only get up to 3 spells of a particular level at a time, but they keep most of their power, and get the benefit of being able to cast like a spontaneous caster, for the most part. I'm sure this is terribly abusable in a high-op game, but it's never been a problem for me.
Best Answer
Strict RAW - No
In D&D 5e spells do only what they say in their description nothing more or less.
Nothing in the spell description for alarm says or implies that a magic user would understand the difference between the alarms they set. This means that a strict RAW reading would mean that a caster cannot do what OP wants.
Personally, and this is solely my opinion, I do not think this is the best way to adjudicate this as it seems needlessly legalistic and goes contrary to the ethos of enabling players to do fun things in general.
Rules as Interpreted - Assumed player choice
An arguably more lenient interpretation of RAW brought up by @TimGrant in their answer says that it is implicit that when the spell says "an alarm" and "a hand bell" that the spell is allowing room there for player choice in the matter. Examples of other spells might be using misty step to teleport to “an unoccupied space” and polymorph transforming a creature into "a new form". It may not be provable or definitive, but it makes sense and allows for creative and clever uses of the spell.
Rules as Fun - Yes
I don't see anything game-breaking or even close to it by allowing the spellcaster to know the difference or even to tweak the sound of the audible alarm. In fact, it makes a lot of sense intuitively that the spell would work this way in-universe even if the RAW doesn't support that.
This is a perfect example of a case where the DM plays an important part in adjudicating the rules in the game. In this case, they get to determine whether or not to allow a player to go slightly out of bound of the precise wording of the spell description. And this is perfectly good and encouraged by the designers.
In this case, I would rule this a clever use of a spell without any game-breaking potential and would not hesitate to allow it at my table. I can't think of a single reason that allowing it would be detrimental to any game.
Bonus: Using multiple alarms to get the same effect using only RAW
If the DM is insistent upon following the strict RAW and disallowing the caster knowledge of which mental alarm goes to where, there may still be a clever way to get the desired effect. @BaconHero in their answer said that if you place several alarm spells close to each other in very clever ways you can use that to let the caster know which way they are coming from. For example, you could place one alarm spell on the door to passage A, another on the door to passage B, and another just inside of the door to passage B. Thus, the caster will hear 1 ping if a creature is coming from A and two if one is coming from B. If the caster is very careful and precise about placing the spells, they can get useful directional information.