According to the official site:
The event has been held under a number of different names since the first summer under-18 tournament in 1991 – the Phoenix Cup – in Yokohama and Sapporo, Japan.
It was played for three years in Japan, went to Mexico City in 1994, back to Japan in 1995 and to Nelson and Castlegar, B.C., in 1996 before settling into the Czech Republic and Slovakia beginning in 1997. It alternated between the countries from 1997-2001 before the neighbours co-hosted from 2002-17.
The tournament was known as the Junior World Cup before it was renamed in honour of Ivan Hlinka following the tragic passing of the Czech hockey legend in a car accident in 2004. Hlinka won three IIHF World Championship gold medals as a player before leading the country to Olympic gold as head coach in 1998, among his many accomplishments and accolades.
When the tournament returned to Canada in 2018 (in Edmonton and Red Deer), it was rechristened the Hlinka Gretzky Cup, honouring Hlinka and The Great One himself, Wayne Gretzky.”