How can you selectively dispel spells?

Question

Suppose an enemy have blur and slow cast on them.

Can I use dispel magic to end the magical effect blur, without dispelling slow?

---

The above spells are just examples. This question mainly ask about how dispel magic can be used to end one spell affecting a creature without dispelling other spells.

What are the conditions must be satisfied to do this? Does the will-be-dispelled spell must have a perceivable effect to be able to be targetted? Does the spell must be lower than dispel magic? Must I name the spell I wish to end? Must I name the effect ("whatever making him looks blurry")?

Answer 1

You can remove spells one at a time, but only when targeting particular effects.

It's pretty clear that when targeting creatures or objects, you have no real control over which spells end. So what's left is that "magical effect" wording.
But what does a "magical effect" mean?

Dispel Magic does actually give us some guidance here - in its Higher Levels text.

...you automatically end the effects of a spell on the target if the spell's level is equal to or less than the level of the spell slot you used.

It is a safe assumption that Dispel Magic doesn't wildly change how it works when casted at a higher level. That means that this text in the main body of the spell:

Any spell of 3rd level or lower on the target ends.

Can be restated as "The effects of any spell of 3rd level or lower on the target ends".
That clearly shows that spells - even those that target creatures or objects - produce an "effect". And, because spells are magic, those effects are "magical effects".

Therefore, you can individually target magical effects - even those produced by spells targeting creatures - to get rid of specific spells, at a rate of one effect per casting of Dispel Magic.

Answer 2

You can dispel any magical effect you are aware of, but only if you have a clear path to it

First, the important part of dispel magic:

Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends.

Targeting a creature

If you target a creature, your only option is to (attempt to) dispel every spell on that creature. In this case, "any spell [...] on the target" is intended to be read as "each of the zero or more spells [...] on the target".

Targeting a magical effect

Clear path

The rules on targeting spells say:

To target something, you must have a clear path to it, so it can't be behind total cover.

This doesn't just apply to creatures, so you must have a clear path to the magical effect in order to target it. The standard cover rules (including weird edge cases like windows and wall of force) have been covered in many other questions. The interesting question for dispel magic is: to which magical effects can you have a clear path?

You certainly have a clear path to shield of faith, since a "shimmering field appears and surrounds a creature". On the flip side, nothing in the description of death ward indicates that it is present in any way; after all, spells only do what they say they do. I would therefore conclude that death ward cannot be directly targeted, because it isn't present in a way that allows for a clear path. You could still target the creature, just not the effect itself.

Choosing

Unlike many other spells, dispel magic allows you to choose any target, even one you can't see. That said, you still have to choose a target.

Spells that produce a visual effect (blur, fire shield) are clearly choose-able. Any creature affected by zone of truth is "aware of the spell", and thus could choose to dispel it, despite the lack of visual effect. A creature that correctly identifies a spell (via an ability check as it is cast or identify) could choose to dispel an otherwise-imperceptible spell, like aura of vitality, so long as the creature has a clear path to the effect.

The rules don't say that you need to know exactly what spell you are dispelling. Therefore, dispelling "the 7th-level hallow spell I just identified" is just as acceptable as "whatever these tentacles are". If you try to dispel something that isn't a spell, it just doesn't work. Similarly, if you choose "the invisibility on the creature in that square" and there is no creature in that square, it just doesn't work.

Conclusion

In order to dispel an individual effect, you must both...

1. Have a clear path to the effect.
2. Be aware of the effect (enough to precisely target it).

In your specific example, blur qualifies for both points. You can certainly be aware of slow, but a clear path is trickier:

You alter time around up to six creatures of your choice in a 40-foot cube within range.

Unlike, say cloudkill, slow doesn't actually create an effect that fills the 40-foot cube. Rather, targets are chosen from within that area. That said, the fact that you "alter time around up to six creatures" leads me to believe that there is an invisible area of slowed time surrounding each target. Therefore, you can have a clear path to the effect. (The wording is really important here. If slow said that you alter time for creatures, I would say that you don't have a clear path.)

As a result, you can dispel slow or blur selectively (by targeting an effect), or you can dispel them both (by targeting the creature).

Answer 3

You can’t

You have to:

Choose one creature, object, or magical effect within range.

To target a “magical effect” it has to be a ‘free standing’ spell like an illusion. If the target of a spell is a creature, you have to target the creature which means it will potentially affect all spells on the creature.