You must report to the school whose I-20 or DS-2019 you use to enter the U.S. and meet their enrollment requirement or you will be in violation of your student status.
Your SEVIS record will need to be transferred from your current institution to UNH. NOTE: This is a transfer in terms of immigration and is separate from any type of academic transfer process.
NOTE to Canadian Students: While you are not required to obtain a visa, you are required to present your Certificate of Eligibility and declare yourself as a student at the U.S. port-of-entry.