There is a lot of confusion regarding high school students who want to play a varsity sport that their high school does not offer. With special circumstances that can happen, but it is rare, and the student must almost always reside in the school district they want to play for (the “parent’s district of residence” is the term the rules use).
One example of being allowed to play for a different high school is if the student resides in the Beavercreek school district but goes to Carroll High School. Most likely and as long as Carroll does not have a high school hockey team, the student can play for Beavercreek. If that student went to Alter, they would have to play for Alter since Alter has a high school hockey team.
Again, the main factor is almost always that the student must reside in the school district they want to play for.
With very few exceptions for home-schooled students (and there is a very specific definition for “home-schooled student”) a student may be able to play for a different school than their residential school district, but there are VERY specific rules.
The Ohio High School Athletic Association (OSHAA) governs Beavercreek high school sports and sets the eligibility rules for Beavercreek Varsity Ice Hockey. Below are the links to the OSHAA website with their eligibility rules and guidelines. Also listed is the contact information for the Beavercreek High School Athletic Office and Athletic Director. If you have any questions, the Beavercreek Athletic Director should be who you contact first.
Beavercreek High School Athletic Director: Brad Pompos, 937-458-2454, firstname.lastname@example.org
Assistant Athletic Director: Bob Beekman, 937-458-2584, email@example.com
Athletic Office Secretary: Deanna Fecher, 937-458-2465, firstname.lastname@example.org