Yes, Lord Vishnu is also called Shiva in few versions of Vishnu Sahasranama. For example, Shiva appears as 27th name in Vishnu Sahasranama found in Mahabharata: Anusasana Parva:
17 सर्वः शर्वः शिवः सथाणुर भूतादिर निधिर अव्ययः
संभवॊ भावनॊ भर्ता परभवः परभुर ईश्वरः
17 sarvaḥ śarvaḥ śivaḥ sthāṇur bhūtādir nidhir avyayaḥ
saṃbhavo bhāvano ...
Vishnu appears in different colors in different yugas. This is mentioned in Mahabharata Vana Parva (3.148). Here I am presenting the (edited) translation of van Buitenen -
Hanumān said: That Eon is called the Winning Throw, my friend, in which the sempiternal Law holds reign. In that age, that best of Eons, things are done, not left to be done. There the ...
As you have already stated in the question, Bhishma told Vishnu Sahasranama to Pandavas. To be more precise, it was Yudhushtira who asked for it. The names present in the stotra are the most famous names of Lord Vishnu which were already sung by great men and rishis.
yāni nāmāni gauṇāni vikhyātāni mahātmanaḥ|
ṛṣibhiḥ parigītāni tāni vakṣyāmi ...
Adi Shankara didn't quote from Bhagavatam in any of his commentaries. So, it is likely that he may be referring to verses from Vishnu Purana (5.13.29-31)
Thus in various actions of Kṛṣṇa the Gopīs imitated him, whilst away,
and beguiled their sorrow by mimicking his sports. Looking down upon
the ground, one damsel calls to her friend, as the light ...