A financial( or fiscal) year can be any 12 month period.
The New England Patroits may elect to operate on a fiscal year , beginning March 1 and ending Feb 28. The reason is, come Dec 31, their year us far from over. There are still playoffs, and a super bowl. This all means income and expenses, and it may make a lot more sense to have all the income and expenses from one season placed into one accounting year.
A calender year system may make sense for a lot of companies, but for others, it might not be the best idea. You cannot change, from one to the other, unless there are compelling reasons.
Most governments opertate on a FY ( fiscal year) starting July 1, because it may take several months after 12/31 to receive and account for all the tax money that is due them.