Generic term is therianthropy:

therianthrope – wild beast (therion) + man (anthropos)

lycanthrope – wolf (lykos) + man (anthropos)

arctanthrope – bear (arktos) + man (anthropos)

tigranthrope – tiger (tigris) + man (anthropos)

kaprothrope – boar (kapros) + man (anthropos)

arouranthrope – rat (arouraios) + man (anthropos)

lamianthrope – shark (lamia) + man (anthropos)