Why Devi Is Called Durga?

दुर्गायै दुर्गपारायै सारायै सर्वकारिण्यै।
ख्यात्यै तथैव कृष्णायै धूम्रायै सततं नमः॥
The tenth shloka of the fifth chapter of Durga Saptashati.
Durga:
To understand her is very difficult.
To reach her is very difficult.
She will help you, she will protect you in times of trouble, just drop a hint that you are in trouble, and she will take you out.
But she is not easily accessible like how Sri Krishna is.
Krisha will go after his devotees.
You don't go to him, he will come looking for you.
But Devi is not like that.
Only the most committed, most sincere can merge with her, merge into her.
To be one with her, you have to work very hard.
Durgapara:
She will take you across the worldly troubles which are like an ocean.
She will take you to the other shore.
In times of difficulties, she is there for you, to hold your hand and take you out.
If you are with her then you are at a place where there are no troubles, no dangers.
Sara:
She is the strength in everything, she is at the core of everything making everything stable and strong.
She is the theme of everything.
If there is a story, there is a theme around which the story is developed. This is what we call the essence, the sara.
Devi is the essence, the theme around which the whole world is developed.
Sarvakarini:
She only does everything. She is behind every action in the world.
If you are listening to this now, If I am telling you this now, she is only making you do that, she is only making me do that.
Khyati:
Khyati has got two meanings; khyati means fame, and Devi only is fame. If she is with you, you will become famous.
Khyati is also discretion, power to discriminate between good and bad.
Krishna: Black.
Ponts towards Devi's aspect as Kalaratri, the Goddess of elimination, the goddess of pralaya.
Dhumra:
Dhumra is one of the daughters of Daksha, mother of two Vasus Dhara and Dhruva.
Be it Aditi, Diti, Dhumra; they are all her own various forms.
Namaskaras to her.
अतिसौम्यातिरौद्रायै नतास्तस्यै नमो नमः।
नमो जगत्प्रतिष्ठायै देव्यै कृत्यै नमो नमः॥
Sowmya: gentle, soft. Like Somadeva. Like the moon.
Atisowmya: most gentle, most soft.
Roudra: ferocious.Like Rudradeva. Like fire.
Atiroudra: most ferocious.
Who is she Atisowmya with?
With those who respect her, take shelter in her, her devotees.
Who is she Atiroudra with?
With the evil, with the wicked.
नताः- means we bow before her.
Jagatpratishta: Foundation of the world. The world is resting upon her.
We say democracy is the foundation of our country.
Our entire system is built upon the foundation called democracy.
The whole world, the whole universe is built upon the foundation called Devi.
Meaning of Devi, we have already seen.
Krityai: Kriti means action.
The force behind action, the power behind action, that is her, that is Devi.
या देवी सर्वभूतेषु विष्णुमायेति शब्दिता।
नमस्तस्यै नमस्तस्यै नमस्तस्यै नमो नमः॥
Bhuta means whatever has come into existence.
Objects, beings, forces, energies, emotions, thoughts everything.
What is Vishnumaya?
अव्यक्तं व्यक्तरूपेण रजःसत्वतमोगुणैः।
विभज्य यार्थं कुरुते विष्णुमायेति सोच्यते॥
The avyakta, the unmanifest, the homogenous state before creation, whatever divides that into satwa, rajas, and tamas and makes everything perceivable, as we see and sense everything around us, that whatever is Vishnumaya.
The manifested world is Vishnumaya.
Devi is Vishnumaya.
She is the power of Vishnu with which he brings the world into existence.
Why namastasyai three times?
In poetry, this is a technique called Repetition.
Used for rhythm or to emphasize something.
Here in Durga Saptashati, repetition of namastasyai has a different purpose.
The entire universe is based on the concept of triads.
Like the three gunas, the Trimurthys, three states solid-liquid-gas, three worlds bhumi-antariksha-swarga.
The threefold nature of Devi is at the foundation of all these.
Namaskaras are offered separately to each of these three aspects of Devi.
प्रसादने संभ्रमेऽपि द्विस्त्रिरुक्तं न दुष्यति
You can repeat if you want to please someone.
We say: You look so nice, so nice.
Or please do it, please do it, please do it.
You also repeat when you are overwhelmed about something.
It's so huge, so huge..
Here you want to make Devi happy, so you are repeating your namaskaras.
namastasyai....
see namaha 5 times in one shloka itself.
And because you are overwhelmed about her greatness.