Yes. The name "Trinity" in God signifies the determinate number of persons because the plurality of persons in God requires that we should use the word trinity: i.e., what is indeterminately signified by plurality, is signified by trinity in a determinate manner.
In its etymological sense, this word "Trinity" seems to signify the one essence of the three persons, according as trinity may mean trine-unity. But in the strict meaning of the term it rather signifies the number of persons of one essence; and on this account we cannot say that the Father is the Trinity, as He is not three persons. Yet it does not mean the relations themselves of the Persons, but rather the number of persons related to each other.
In the divine Trinity not only is there unity of order, but also with this there is unity of essence.