@PotomacBob
Thus a fiscal year the begins on October 1, 2023, is named fiscal year 2024.
Does that same logic apply to seasons? Is the season that begins December 1, 2023
It is not quite that simple. The example you are showing is the Fiscal Year of the US Federal Government, but not everybody follows that. Most states work from July to June (because July is traditionally the first full month with no school and that is commonly one of their largest expenditures). Most businesses work from January through December as that is when taxes are computed.
The US Government also used to use the July through June model, but moved to October in 1976. The move was for many reasons, including the end of a budget control act that year, as well as to give Congress more time to hash out the budget for the next year.
But yes, it is named after the year in which most of it occurs, and not when it starts. And most systems use that tradition. The PGA (golf) runs from September through August, but as most of the season in play right now happens in 2023 so it is known as the 2023 season, even though it started in 2022. The NBA follows the same naming scheme as does the NHL and all other sporting leagues that I am aware of.
However, Baseball does not as the entire season is within a single year. Football only has finals in another year, so the last Superbowl was the end of the 2022 season, even thought it ended in 2023.
For the weather season, I suspect it is tied to both because the seasons of hurricanes in the Atlantic and Pacific as well as typhoons in the Indian Ocean as well as other storm cycles often straddle the traditional year endings with many of them overlapping.