As a youth, Ivan played
ice hockey for the club
HC Vítkovice Ridera. He was a member of the under-16 team from 2015 to 2018, appearing in 67 games and scoring 65 points (37 goals, 28 assists). After playing 62 games and scoring 22 points for the Eagles, he returned to the Czech Republic during the
COVID-19 pandemic and appeared in five games in the Czech second-tier for
AZ Havířov. Ivan then went back to Canada for the 2021–22 season, being the leading point scorer (65), goal scorer (31) and joint-assist scorer (34) for the Eagles in 61 games played. In 2022–23, Ivan led the Eagles in all three categories, having a career-best 90 points, 33 goals, and 57 assists in 64 games, being among the top 10 in the QMJHL in points and assists. He concluded his Eagles career with 191 regular season games played, 177 points, 75 goals and 102 assists. He appeared in 67 games and registered 31 points (12 goals, 19 assists). Although initially reassigned to the Eagles for the 2024–25 season, he was recalled from the AHL before NHL season's opening night. Ivan made his NHL debut on 9 October, against the
Vegas Golden Knights, playing just under 10 minutes. In doing so, he became the first NHL player in history to have the same first and last name. Ivan scored his first NHL goal on 24 October, assisted by
Nathan MacKinnon and
Casey Mittelstadt. ==International play==