The usage of an article depends on the specific context—and what you intend the sentence to convey.
Context #1: Words as Words
The word for that red fruit is apple.
Here, apple is not being used within the sentence functionally but as a word. You could describe it as playing a "meta" role within the sentence.
As described by The Chicago Manual of Style (17th ed), 7.63:
When a word or term is not used functionally but is referred to as the word or term itself, it is either italicized or enclosed in quotation marks.
Although that discusses how such words or terms should be styled, the discussion of its syntactical role is what's important here.
In contrast, neither of the following constructions would be correct:
The word for that red fruit is an apple.
The word for that red fruit is an apple.
Because you are referring to apple as a word, putting an article in front of it is inappropriate. (And it is not the phrase an apple that is being discussed.)
Taking your example sentence and rephrasing it slightly, we can end up:
The name of this regime is random phase.
Here, random phase is being used as a phrase just as apple was being used as word.
Further, neither of these analogous constructions would be correct:
The name of this regime is a random phase.
The name of this regime is a random phase.
Context #2: Words as Functional Components
I am holding an apple in my hand.
Unlike in the first context, apple is now serving a functional role within the sentence itself. As such, the article is appropriate.
Removing the article would result in a construction that was incorrect (assuming it's still the same single apple):
I am holding apple in my hands.
Again, rephrasing your example sentence, we can end up with:
This is a random phase.
Removing the article would result in something similarly incorrect:
This is random phase.
Disambiguation: Your Example Sentence
Here is your actual example sentence:
This regime is called random phase.
You need to ask yourself in what way you are using the phrase random phase. Is it being used as a phrase (Context #1) or is it being used as a functional component (Context #2)?
The problem is that your sentence construction isn't as explicit as the constructions I've been using. Therefore, random phase sometimes sounds correct with the article in front of it, and sometimes sounds correct without it.
While you can use what sounds right to you (the problem is that the two of you disagree on what that is), it's more logical to place it within the correct interpretation and then use the syntax that would be appropriate for that unambiguous interpretation.
Context #1:
(This regime is called random phase.)
The name of this regime is random phase.
The term for this type of regime is random phase.
Random phase is what this regime is referred to as.
Context #2:
(This regime is called random phase.)
This regime is a random phase.
This is a random-phase regime.
This is a random phase type of regime.
There is also nothing wrong with defining the term (or name) on its first use (Context #1), and then referring to it directly in subsequent uses just as you would any other noun.
Note that even though I used the indirect article in my examples, if random phase is a unique (or singular) item, then the direct article can be used. And if it is actually a proper noun, it's common (although not necessary) to capitalize it (as in the Random Phase or The Random Phase).
In every-day English, “This regime is called random phase” appears to cry out for an article, almost certainly “the” but it’s not truly necessary, as should be evident from the second example.
For future reference, all other things being equal, everyone should trust German before Czech ideas about English articles.
– Robbie Goodwin Jul 30 '18 at 15:46