In Daniel 1, it would appear that Daniel, Hananiah, Mishael, and Azariah were trained for 3 years before first meeting with and being found faultless by Nebuchadnezzar. However, in Daniel 2, Daniel interprets the king's dream in year 2 of his reign, and has his three friends promoted by the king. So the king would have already known them by the time their training was over.
The year in which Nebuchadnezzar came to the throne is his accession year. His year 1 begins at the Babylonian New Year (1 Nisannu) following his accession. His year 2 begins at the next Near Year. So theoretically it is possible that the three-year “training” began during his accession year and finished towards the end of year 2.