In his youth, Rav Nachman studied together with Rava, but he sat one row behind him. Later Rav Nachman studied under Rav Chisda. During the time when Rav Joseph bar Chiya was head of the Yeshivah of Pumbeditha and Rava conducted his own Yeshivah in Mechoza, Rav Nachman bar Yitzchak was the chief lecturer (Resh Kalah) under Rava, and he was already famous for his great learning and piety.
Legend states that a soothsayer predicted to Nachman's mother that her son would be a thief. She was therefore very careful to instill in him a fear of heaven. She often reminded him: "My son, cover your head completely, so that you will fear G-d, and always pray for his mercy, so that you should not be overcome by your evil impulses". It is told that once while studying under a tree, his headcovering slipped off, and he suddenly felt a tremendous desire to take a cluster of dates from the tree (which did not belong to him). (Shabbos 156b)
He praised the character trait of humility greatly. His modesty may be seen from the fact that when Rava stated that "a little pride is becoming a scholar," Rav Nachman hastened to remark, "None of it, nor part of it!"
He worked to facilitate a peaceful relationship between husband and wife.
The honour of the Sabbath was of prime importance to him. He would even personally do menial chores in its honour. He would say that "one who honours the Sabbath will be saved from the pains of the exile".
He had a quick wit often using the double entendres as a mnemoic device.
It is unclear which of the three sages called Nachman are referred to when R' Nachman w/o a surname is mentioned. However, the fact that Rav Nachman bar Yitzchak often states a position after R' Nachman (w/o surname) should allow us to rule him out. (Tosafot to Tractate Chullin)