Question:
Answer:
You inquire about the central mystery of the Catholic faith and the most profound one as well (although Our Lord’s hypostatic union is a close second).
The simple answer is that, yes, each Triune person has a personality, as the Catholic Encyclopedia affirms, and their respective personalities are simply as Father, Son, and Holy Spirit. In this case, we see the term personality is used to affirm and distinguish their each being distinct, divine persons, while each also wholly possesses one divine nature. Personality is not meant in the typical merely human sense, e.g., choleric, sanguine, melancholic, or phlegmatic.
For more on this great mystery, see the Catechism of the Catholic Church (232ff.). In addition, we have a variety of free online resources for you to browse.