В данном случае слово "отделение" можно опустить, так как мы уточняем место расположения УФМС, что и подразумевает отделение этой службы в конкретном регионе.

Если же сочетании Russian Federal вас смущает, его возможно перевести как Federal Migration Service of Russia or Russia's Federal Migration Service

С официального сайта:

Having reasonable grounds for visa extension a foreign citizen applies to a territorial department of the Federal Migration Service in person. The application for the visa extension should be submitted before the visa expiry.
http://www.fms.gov.ru/useful/formvisa/index_eng.php

i think you need to mention "Department",
also see here:
http://www.proz.com/kudoz/russian_to_english/law_general/432...

and to Oblast/region here:
http://www.proz.com/kudoz/russian_to_english/education_pedag...

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Note added at 8 hrs (2011-05-24 12:06:09 GMT)
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eg.:
Territorial form of the Department of the Federal Migration Service for the Republic of Karelia it is created for implementation of law enforcement duties, functions of control, supervision and rendering national assistance in the sphere of migration, as well as for realization of independent tasks and functions of the Federal Migration Service established by legislative and other normative legal acts of the Russian Federation.
http://www.gov.karelia.ru/Power/Office/Migration/index_e.htm...