The appropriateness of this name may be shown in two ways.
Firstly, from the fact that the person who is called "Holy Ghost" has something in common with the other Persons. For, as Augustine says (De Trin. xv, 17; v, 11), "Because the Holy Ghost is common to both, He Himself is called that properly which both are called in common. For the Father also is a spirit, and the Son is a spirit; and the Father is holy, and the Son is holy."
Secondly, from the proper signification of the name. For the name spirit in things corporeal seems to signify impulse and motion; for we call the breath and the wind by the term spirit. Now it is a property of love to move and impel the will of the lover towards the object loved. Further, holiness is attributed to whatever is ordered to God. Therefore because the divine person proceeds by way of the love whereby God is loved, that person is most properly named "The Holy Ghost."
And by adding the word "holy" we signify the purity of divine goodness. But if Holy Spirit be taken as one word, it is thus that the expression, in the usage of the Church, is accommodated to signify one of the three persons, the one who proceeds by way of love.