Προσπαθώ να αλλάξω τη δική μου συμπεριφορά όταν έχω άγχος.

Να is a particle that introduces the subjunctive form of the verb. Modern Greek doesn’t really use an infinitive like English “to change”. Instead, it uses:

• προσπαθώ να αλλάξω ≈ “I try to change”

So να + verb (subjunctive) often corresponds to English “to + verb” or “that I + verb”.
Here, να is required after προσπαθώ to introduce what you are trying to do.

Both come from the same verb, but:

• αλλάζω = present subjunctive (ongoing / repeated action)
• αλλάξω = aorist subjunctive (single, complete action)

In this sentence:

• προσπαθώ να αλλάξω τη δική μου συμπεριφορά
  → “I try to make a (one-off / decisive) change in my behavior.”

If you said:

• προσπαθώ να αλλάζω τη συμπεριφορά μου
  it would suggest “I try to be (constantly) changing my behavior / changing it habitually,” which is a different nuance and less natural in this context.

Greek articles change form depending on the grammatical case:

• η συμπεριφορά = nominative (subject)
• τη(ν) συμπεριφορά = accusative (direct object)

In this sentence, συμπεριφορά is the object of να αλλάξω (“to change my behavior”), so it must be in the accusative:

• να αλλάξω τη δική μου συμπεριφορά
  (not η δική μου συμπεριφορά here)

Yes, both relate to possession, but they play different roles:

• μου is the ordinary weak possessive pronoun = “my”
• δικός / δική / δικό (μου) is an emphatic possessive = “my own / mine”

So:

• η συμπεριφορά μου = “my behavior”
• η δική μου συμπεριφορά = “my own behavior” (as opposed to someone else’s)

You almost always use δικός / δική / δικό together with μου, σου, του, της, μας, σας, τους, not alone. So ✗ η δική συμπεριφορά is wrong; it must be η δική μου συμπεριφορά.

Yes:

• να αλλάξω τη συμπεριφορά μου = “to change my behavior”

This is perfectly correct and more neutral.
τη δική μου συμπεριφορά adds emphasis:

• “to change my own behavior” (implying “instead of focusing on others’ behavior,” or highlighting the contrast).

The emphatic possessive δικός / δική / δικό agrees in gender, number, and case with the noun it refers to:

• συμπεριφορά is feminine, singular, accusative.
• So the matching form is δική (feminine singular accusative).

Examples:

• ο δικός μου φίλος (masc) – “my own friend”
• η δική μου συμπεριφορά (fem) – “my own behavior”
• το δικό μου σπίτι (neut) – “my own house”

In Greek, when you use this emphatic possessive structure, the typical pattern is:

article + δικός/δική/δικό + weak possessive + noun

So you get:

• τη δική μου συμπεριφορά
• τον δικό σου φίλο
• το δικό μας σπίτι

You don’t say ✗ δική μου τη συμπεριφορά. The article belongs to the noun phrase as a whole and comes before δική.

The full accusative feminine article is την, but in practice:

• Before most consonants, it is usually written and pronounced τη.
• Before vowels and certain consonants (κ, π, τ, ξ, ψ, μπ, ντ, γκ, τσ, τζ), many writers keep την.

Here, συμπεριφορά starts with σ, so it’s standard to write:

• τη συμπεριφορά

You may also see την συμπεριφορά in some texts, but τη συμπεριφορά is the common modern spelling.

Άγχος here is treated like an indefinite / abstract noun (similar to “stress, anxiety” in a general sense). Greek often drops the article in such expressions:

• έχω άγχος = “I have (some) anxiety / I am under stress”
• έχω δουλειά = “I have work (to do)”
• έχω χρόνο = “I have time”

If you said έχω το άγχος, you’d be talking about some specific anxiety already known from the context (“I have the anxiety [we mentioned]”), which is not what’s intended here.

Both can be translated as “I am anxious / stressed,” but there is a slight nuance:

• έχω άγχος (lit. “I have anxiety”)
  – very common, sounds general and can refer to being stressed, worried, under pressure.

• είμαι αγχωμένος (lit. “I am anxious-stressed”)
  – focuses more on your current emotional state, “I am feeling anxious / stressed right now.”

In many everyday situations they are interchangeable:

• Όταν έχω άγχος, …
• Όταν είμαι αγχωμένος, …

Both are natural; the sentence you gave just uses the common fixed phrase έχω άγχος.

Yes, that’s completely natural:

• Όταν έχω άγχος, προσπαθώ να αλλάξω τη δική μου συμπεριφορά.

Greek word order is flexible, and placing the όταν-clause first is very common. The meaning stays the same; it just changes the emphasis slightly (starting with the condition).

Συμπεριφορά means “behavior, conduct, way of behaving.”

It comes from συμπεριφέρομαι = “to behave.” There isn’t a direct, obvious English cognate, so it’s a word you mostly have to memorize.

Examples:

• Καλή συμπεριφορά – good behavior
• Κακή συμπεριφορά – bad behavior
• Η συμπεριφορά του στη δουλειά – his behavior at work

Άγχος is pronounced approximately like [Á-nghos]:

• άγ-: the γ before χ is a voiced velar fricative, merging into the χ sound. For learners, you can think of it as a “soft g” that blends into “kh.”
• -χος: like “khos” (a hard h from the back of the throat, then “os”).

So, slowly: Á-nghos, with the stress on the first syllable: Ά-γχος.