If yes, what justification they provide? Please quote their original works.
Vedanta Desika is fairly clear that the term Narayana is unambiguous.
In the Tattvamuktakalapa 3.5 Desika states:
nissādhāraṇya-nārāyaṇa-pada-viṣaye niścayaṃ yānty-abādhe
sad-brahm-ādyās-samāna-prakaraṇa- paṭhitāś śaṅkitānyartha śabdāḥ।
antaryantā ca nārāyaṇa iti kathitaḥ; kāraṇaṃ cāntar-ātmety
asmād-apy-aika kaṇṭhyam bhavati nirupadhis tatra śambhvādi śabdāḥ॥
In his own commentary on the Tattvamuktakalapa known as the Sarvartha Siddhi, in the context of the current verse, Desika states:
sad-śabdastāvat sattāyogiṣu sarveṣu pravṛttatayā na viśeṣa nirdhāraṇārhaḥ। brahmaśabdaḥ ekarūḍho'pi bahuṣu rūḍhavat prayuktatayā anyārthatva śaṅkārhaḥ syāt। ātmaśabdasca jīva-parādhi-sādhāraṇa-prayogaḥ। evaṃ puruṣa-prāṇ-ākṣara-śabdā api।
nārāyaṇaśabdastu na jātyupādhivacanaḥ, na vā'nekarūḍhaḥ। atastena anyeṣām viṣaya-viśeṣaṇa-nirdhāraṇam yuktam। tatra ca hetuḥ samāna-prakaraṇa-paṭhiṭatvam। anyathā paśvadhikaraṇāderapi bhaṅgassyāt।
- The word sad cannot connote a specific entity as it is used to refer to the ordinary jagat by the Sarvajñasattāvādins.
- The word brahman although has a commonly understood single sense, it is applied in reference to multiple entities commonly. Therefore it cannot be used in a unique manner as it can cause confusion.
- The word Atman is used normally in many senses to refer to the jIva as well as the paramAtman.
- Similarly, words like puruSha, prANa, akShara also are incapable of denoting a unique entity.
- Unlike these, the word Narayana is neither used a descriptor of categories (jāti) nor attributes (upādhi).
- Nor is it commonly/popularly used to refer to many different things.
- Therefore it is proper (not ambiguous) for it to have a object-attribute relationship with other words (other words are the attributes).
- This is because of it (the word Narayana) being used identically (as the other words like sad, brahman, etc.) in the same context (where the other word appears).
- Otherwise chAga-pashu-nyAya and others would breakdown. (This refers to the principle of interpretation laid down by the Mimamsakas: when multiple terms are used in the same context, the term having a general meaning should be interpreted to bear the meaning of the term that is most specific.)
From #5 and #6, it is clear that Desika observes Narayana to be a term that is seen to be consistently applied (in extant scripture) to identify a unique entity and none else (either as a category or attribute or popular usage). The consequence of this is that whenever the term Narayana is used alongside other terms within a context in an identical fashion, the application of the principle of chAga-pashu-nyAya (#9) becomes appropriate. Thus in a context where both the term Narayana and another generic term like Sad, Atman, Brahman etc. are used in an identical manner, it is to be inferred that the other generic terms are used as a reference to Narayana.