Ez az úgynevezett új terv.

They are two separate things:

• ez = this
• a / az = the

In Hungarian, when this or that comes directly before a noun, the definite article is usually kept:

• ez a terv = this plan
• az a terv = that plan

So ez az úgynevezett új terv is the normal Hungarian pattern for this so-called new plan.

Depending on context, the whole sentence can also mean This is the so-called new plan.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

The next word here is úgynevezett, which starts with the vowel ú, so the article must be az:

• ez az új terv
• ez a régi terv

In Hungarian, the verb to be is often omitted in the present tense, third person when the sentence identifies or describes something.

So:

• Ez az új terv. = This is the new plan.
• Ez egy jó ötlet. = This is a good idea.

Hungarian does not normally say Ez az új terv van in this kind of sentence.

úgynevezett means so-called.

It can be:

• neutral, meaning commonly called
• slightly skeptical or distancing, like English so-called

So az úgynevezett új terv can mean:

• the plan that is called new
• or the “new” plan, possibly with some doubt or irony, depending on tone and context

Hungarian adjectives usually come before the noun, and more than one modifier can appear there.

Here:

• úgynevezett = so-called
• új = new
• terv = plan

The order az úgynevezett új terv most naturally means:

• the so-called new plan

In other words, úgynevezett is understood as modifying the whole phrase új terv.

If you changed the order, the meaning or emphasis could shift, and it would often sound less natural.

It behaves like one here, yes.

More exactly, it is historically a participle-like form from the verb nevez (to call, name), but in modern Hungarian it often functions just like an adjective before a noun:

• az úgynevezett módszer = the so-called method
• az úgynevezett új terv = the so-called new plan

So for a learner, it is very practical to treat it as an adjective-like modifier.

Yes, it is written as one word.

It is built from:

• úgy = so, thus
• nevezett = called / named

So the original idea is roughly called that way or thus-named, which developed into the standard meaning so-called.

You do not normally split it up in this use.

Because Hungarian adjectives in front of a noun usually do not agree with the noun in number or case.

So you get:

• új terv = new plan
• új tervek = new plans
• új tervet = new plan (object)

The adjective új stays the same. The same is true for úgynevezett:

• úgynevezett új terv
• úgynevezett új tervek
• úgynevezett új tervet

The endings usually go on the noun, not on the adjectives before it.

A very useful example is the accusative (direct object):

• ezt az úgynevezett új tervet

This means this so-called new plan as an object, for example in a sentence like:

• Látom ezt az úgynevezett új tervet. = I see this so-called new plan.

Notice what happens:

• ez → ezt
• az stays az
• terv → tervet

Hungarian often marks the case on both the demonstrative and the noun in this kind of structure.