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 it automatically invokes the application of the principle of chAga-pashu-nyAya (#9) in interpreting the contexts where both the term Narayana and another generic term like Sad, Atman, Brahman etc. are used in an identical manner.