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According to Panini, Sanskrit grammar says that the "Na" in "Narayana" turns it into a proper noun. A proper noun applies to that specific being unlike a common noun, like Shiva, which can apply to anyone since it just means "auspicious."

So, if a verse says "Narayana created the universe," and another verse says "Shiva created the universe," then "Shiva" in that verse actually means Narayana, since "Shiva" is just a common noun, so that that verse would mean "The auspicious one created the universe."

Do Shaivas or Shaktas refute that Narayana is a proper noun?

Panini 8.4.3 says nouns which are made of two words (need not be proper nouns), न (na) in second word changes to ण(ṇa), if first word has र (ra) or ष (ṣa) but not ग (ga),

Sutra just says Nouns not proper nouns. This rule is also present in other Indian languages like Telugu. Same is said in this page.

When two words are joined, according to pAnini's grammar, it becomes
nArAyaNa (नारायण) and not nArAyana (नारायन)

Each sanskrit word has many meanings and nArAyaNa is no exception.
nArAyaNa means the one who gives shelter to nAra (jIva-s). This
meaning is called as 'yougika' (यौगिक) meaning. It is a raw meaning of
the word and does not point it to any particular identity. yougika
meaning the meaning derived by joining two words (yOga).

There is another meaning called as rUDhi (रूढि) meaning. It means the
obvious meaning.

When we say surpaNakhA. nakha means nail. surpaNakhA means the one
which big nails (long nails). This is the yougika (यौगिक) meaning. But
by saying surpaNakhA, we only and only mean rAvaNa's sister and not
any other identity. In other words, whenever surpaNakhA is used, it
'obviously' means rAvaNa's sister surpaNakhA. this obvious meaning is
called as rUDhi (रूढि) meaning.

Scriptures and some commentators describes word "Narayana" as attribute only.

For example, here is what Sri Bhaskaraya, one of the finest SriVidya Acharyas, says about Narayana in his Lalitha Sahasranama Bhasya:

नारायणी नादरूपा नामरूप-विवर्जिता ।
ह्रींकारी ह्रीमती हृद्या
हेयोपादेय-वर्जिता ॥ ७०॥

nārāyaṇī nādarūpā nāmarūpa-vivarjitā ।
hrīṃkārī hrīmatī hṛdyā
heyopādeya-varjitā ॥ 70॥

Sri Bhaskaraya's commentary on word Narayani and Narayana: (translated by Anantha Sastry)

Narayana, Vishnu or Siva. The explanation of the word Nārāyana is
given in Manu Smriti (I, 10): "The water is called Narah, because it
emanated from Nara (Brahman) : that is his first abode (ayana), hence
he is named Nārāyana.” The Br. Vaivarta Pr. also, “Because his abode
is among men, hence he is called Nārāyana." The De. Bhāg. Pr.,
"Because Nara means leading, hence, supreme self is called Nara." The
Bhārata, " The wise knows that the Tatvas emanated from Nara (Brahman)
and form his abode, hence he is called Närayana." Here Narayana is
ParamaSiva, because concerning the fourth state, the Kasi khanda Says,
"He is the Husband of Lakshmi and also of Parvati." Or this saying
'the husband of Lakshmi' may indicate non-separation between Lakshmi
and Devi. Or, the sister of Vishnu is called Nārāyani. For there is a
saying, "Adoration in Siva, the husband of Narayani." Or, because
there is no difference Adoration in Siva, the husband of Narayani."
Or, because there is no ilifference between Gauri and Narayana.

In the Kurma Pr. Siva says, “I, the supreme Lord, have divided myself
into two forms, one is Nārāyana, the other is Gaurī, the mother of the
universe. So my supreme nature is known to neither the Devas, nor to
the Rishis, because I am one, I am Devi and Vishnu." The Devi Pr.
says, “Because she has her abode in the water, not in air, or she has
her seat in the ocean, hence she is called Närayani, the creator of
Nara (men) and women." Accorling to the Padma Pr. Närāyani is the name
of the goddess worshipped in the sacred place Supars'va.

He uses the word "Narayana" (Nara + ayana) as attribute to describe it for both Vishnu and Goddess Lalitha.

Actually, references cited by Bhaskaraya provide more info on name Narayana. For example, Medhathithi completely uses the word "Narayana" as Attribute and says it can refer to Brahma in Manu Smriti 1.10.

आपो नारा इति प्रोक्ता आपो वै नरसूनवः । ता यदस्यायनं पूर्वं तेन
नारायणः स्मृतः ॥ १० ॥

āpo nārā iti proktā āpo vai narasūnavaḥ | tā yadasyāyanaṃ pūrvaṃ tena
nārāyaṇaḥ smṛtaḥ || 10 ||

Water is called ‘nara,’—water being the offspring of nara; since water
was the first thing created by (or, the original residence of) that
being, he is, on that account, described as ‘nārāyaṇa.’—(10)

Medathithi proves attribute "Narayana" is also suitable for creator Brahma.

The Being just described is the same who, here and there in the
scriptures, is described under the name ‘Nārāyaṇa,’ as possessed of a
superior degree of creative and cognitive powers, and hence being the
Personal Creator of the world; the mere difference in names does not
necessarily imply difference in the things denoted; so that the Beings
described under the names ‘Brahmā,’ ‘Nārāyana’ and ‘Maheśvara are one
and the same; though they form the objects of diverse forms of
worship, yet they do not differ among themselves; as we shall show
under Discourse XII.

How this is (i.e. how Brahmā is the same as ‘Nārāyana’) is explained
now:—‘Water is called Nara.’—described under the name of,—‘Nara.’

In answer to the objection—“There is no such usage current among
experienced persons; nor is it generally known that water is called
Nara,”—the Author adds:—‘Water being the offspring of Nara,’—the
supreme Being (Hiraṇyagarbha, described in verse 8 as having created
water) might well be known under the name ‘Nara,’ Person; and water is
his ‘offspring;’ hence water is spoken of as ‘Nara,’ the name of the
father is often applied to the child, e.g., the ‘sons of Vaśiṣṭha,’
the revered sages Tāvabhru, Maṇḍu and Lomaka, are spoken of as
‘Vaśiṣṭhāḥ’; and such usage is based upon the

figurative identification of the child with the father.—‘Since’
because—‘Water,’ known as ‘Nara,’ was ‘the first thing created by’—or
it was his container when he lay in the womb (egg)—‘he is, on that
account, described as Nārāyaṇa.’

In the sense of ‘he whose container is Nara’the compound should be
‘narāyaṇa;’ but the first vowel may be taken as lengthened according
to Pāṇini’s Sūtra 6.3.134, which justifies such lengthening in several
other cases also,; just as we have in the word ‘pūruṣa’ (which is a
variant for ‘puruṣa’);—or we may have the lengthening due to the affix
‘aṇ’ in the sense of ‘mass’ [so that nāra would be ‘mass of water,’
and ‘he who has this mass of water as his container, ayana,’ would he
‘nārāyaṇa’]. (10)

So, commentators like Medhathithi says it refers to Brahma also.

Narayana worships Siva, calling him "Narayana" in the Siva Purana. Of course the counterattack would be either Narayanastra ("Tamasic" purana) or Vaishnavastra ("interpolation").

There is a "Vaishnavite" refutation - namely - Varaha Purana

http://om-aditya.ru/userfiles/ufiles/purany/varakha_purana.pdf

Page 90

(The text is corrupted in the source in some places)

23. О three-eyed god, when there was no stem of the uni-verse, and there was no sun, moon or Indra, then you alone re-mained beyond the purview of any reasoning.




24. О lord of gods, wearer of the garland of skulls, bearer of the crescent moon on the head, resorter to the cremationground, smearer of ashes all over the body and encircled byserpents, you are capable of protecting us.




25. You are the Male and the beautiful daughter of the mountain is your Energy. You are fierce to the whole world with your trident, but the three sacrificial fires (Garhapatya, Ahava-nlya and Daksina) remain in your three eyes.




26. In the form of your matted hair remain all oceans, all great mountains and all rivers. The whole universe is your body,though men without proper inner vision see only the physical aspect.




27. You are Xarayana, the source of the universe. Similarly,you are the great Brahma, li.y the difference in the Gunas and difference in the fires and by the difference in the yugas you re-main threefold.




28. О lord, all these chieftains of the gods now seek your favour. О you Rudra, who shine with ashes, we bow to you again,be pleased to save us all.