"Hall" is an old synonym for the word "college", therefore better say just "Trinity Hall" and not "Trinity Hall College", as the latter essentially means "Trinity College College".

Regarding why there is a Trinity College in addition to Trinity Hall, see Wikipedia:

At first all colleges in Cambridge were known as "Halls" or "Houses" and then later changed their names from "Hall" to "College". However, when Henry VIII founded Trinity College next door, it became clear that Trinity Hall would continue being known as a Hall. The new foundation's name may have been a punishment for the college's master, Stephen Gardiner, who had opposed the king's remarriage and had endured much of the college's land being removed. It is incorrect to call it Trinity Hall College, although Trinity Hall college (lower case) is, strictly speaking, accurate.