I am not particularly sure DURING Mahabharata, but in the Bhagavad Purana (Srimad Bhagavatam), there was a clear awareness in Dvarka of Lord Krishna being Bhagavan.
In chapter 11 of the Bhagavatam, Lord Krishna is returning back to Dvarka, and his citizens are welcoming him:
The citizens arrived before the Lord with their respective presentations, offering them to the fully satisfied and self-sufficient one,
who, by His own potency, incessantly supplies others. These
presentations were like the offering of a lamp to the sun. Yet the
citizens began to speak in ecstatic language to receive the Lord, just as
wards welcome their guardian and father.
The citizens said: O Lord, You are worshiped by all demigods like
Brahmā, the four Sanas and even the King of heaven. You are the
ultimate rest for those who are really aspiring to achieve the highest
benefit of life. You are the supreme transcendental Lord, and inevitable
time cannot exert its influence upon You.
O creator of the universe, You are our mother, well-wisher, Lord,
father, spiritual master and worshippable Deity. By following in Your
footsteps we have become successful in every respect. We pray,
therefore, that You continue to bless us with Your mercy.
So it is clear to see that Sri Krishna's citizens know that he is Bhagavan, and so I am assuming that at least a few people knew during Mahabharata.