Shiva means "the auspicious/kind one". The word Shiva is used as an epithet for several Rigvedic deities, including Rudra.
Like other epithets like Indra, Rudra, etc, Shiva is an epithet used to indicate the auspiciousness/kindness of the Almighty God.
In respect of Agni: (RV I.31.1)
तवमग्ने परथमो अङगिरा रषिर्देवो देवानामभवः शिवः सखा | तव वरते कवयो
विद्मनापसो.अजायन्त मरुतो भराजद्र्ष्टयः ||
You, Agni, the frst Aṅgiras, the seer, the god, became a kindly
comrade of the gods. Under your commandment were born the sage poets
working with their know-how—the Maruts with glinting spears.
In respect of Indra : (RV II.20.3)
स नो युवेन्द्रो जोहूत्रः सखा शिवो नरामस्तु पाता | यः शंसन्तं यः
शशमानमूती पचन्तं च सतुवन्तंच परणेषत ||
May Indra, called with solemn invocations. the young, the Friend, be
men's auspicious keeper, One who will further with his aid the singer,
the toiler, praiser, dresser of oblations.
Coming to the aspect of Shiva's manifestation as Sri Dakshina Murty, as a Guru of all Sages which are like embodiment of Dharma tree and who have transcended even Vedas, they are sitting around that Banayan tree, in my opinion, this concept is referring to manifestation of Almighty God.
We have to remember that a Guru of all Sages, which are like embodiment of Dharma tree and who have transcended even Vedas, can only be the Almighty God.
It does not indicate manifestation of Sankara or Husband of Uma as Sri Dakshina Murty, as the term Shiva is an epithet of the formless Almighty God.
Further, Dakshina Murty doesn't indicate facing Southern direction, but indicates propounder/follower of Vedic way of life.