Exactly what you asked for:
for row in enumerate(cursor):
exec("DB{0} = row[1][u'name']".format(row[0] + 1))
This will dynamically create variables DB1, DB2, ..., DBn
But actually you probably want:
x = {"DB{0}".format(row[0] + 1): row[1][u"name"] for row in enumerate(cursor)}
which will actually create a dict with keys DB1, DB2, ..., DBn and values holding database names.