“Personality” has multiple meanings – positive and negative. But the usual (and neutral) meaning is what the Oxford English Dictionary defines as: “The quality or collection of qualities which makes a person a distinctive individual; the distinctive personal or individual character of a person, esp. of a marked or unusual kind.”
We Christians believe that there are three persons in God. Certainly, the union of these persons is a unity-in-distinction. The Son is different from the Father, the Spirit different from the Father and the Son, etc.
This may sound like polytheism, and is considered outrageous by Muslims and others maintaining strict monotheism. But as St. Thomas says, in regard to Muslims’ claim of Christian polytheism, the Muslim misunderstanding is due to their myopic focus on physical generation, and inability to grasp the possibility of purely spiritual generation.
Thus, for the one divine nature, as pure spirit, to be elaborated by Christians as Father, Son, and Holy Spirit, is not contradictory, not to be understood as “three gods.” These three Persons, therefore, are not identical in personality, like clones, and we should not be surprised that they have specific personality characteristics. What can we say about these?
The Son: We Christians, imbued with the religion of the Son, obviously know the most about the personality of Jesus Christ, who came and lived among us, and even a few times offered insights to us concerning his own personal qualities. Conveniently, he describes for us what He is like and how He appeared to others: “Take up my yoke upon you, and learn of me, because I am meek, and humble of heart and you shall find rest to your souls.” (Mt. 11:29)
Occasionally, in the Gospels, Jesus permits evidence of his divine nature and power to shine forth, as in the Transfiguration (Mk. 9:1), or when the guards apprehending Jesus in the Garden of Olives fell to the ground as He identified himself (Jn. 18:6), or in multiple exorcisms in which devils sensed a power emanating from Him.
Most people, however, while marveling at his cures and exorcisms, probably noticed nothing more in his personal presence than a calm and modest preacher. His neighbors asked, Where did this carpenter get such wisdom? We know this fellow and his family. What is going on here? Even Jesus’ cousins didn’t recognize anything special about Him, and didn’t believe in Him until after the Resurrection. (Mt. 13:55-56)
Jesus also tells us about his personal interests in life: not to judge sinners, but to save them (Mt. 9:13), although at the end He will be entrusted by God the Father with the ultimate power of judgment. (Jn. 5:22)
The Father: The New Testament is replete with references to God the Father, but this conception of God as “Father” is also found in the Old Testament: in the Prophets (Is. 63:16, 6:8; Jer.3:4, 3:19) and Psalm 89, but especially in the Book of Wisdom, in which God is described as the “father of the world” who formed the first man (10:1), treats the just in a fatherly way (2:16, 11:11), and governs all things providentially (14:3).
In John’s Gospel, we find that Jesus experienced a constant presence of the Father (Jn. 5:19), speaks about what He learns from this presence (8:38, 12:50), and adds that, in fact, the Father is working through Him (14:10). Jesus, habitually imitating what he sees in the Father, can tell Philip, “he who sees me sees the Father.” (Jn. 14:9)
Jesus’ main descriptions of the Father concern a beneficent Creator, who spreads and maintains all manner of goods in the world, to be used or misused; and is the ultimate solicitous Provider, overseeing even the birds of the air and the lilies of the field, supplying the most intimate needs of all persons, good and bad (Mt. 5:45, 6:8), and like an architect behind the scenes, continually preparing mansions in heaven for the faithful (Jn. 14:2, 20:23).
The Holy Spirit: Although Michelangelo did a marvelous job in depicting God the Father in the Sistine Chapel, in the Gospels the Father only appears as a cloud (Mt. 17:5, Mk. 9:6, Lk. 9:35). The Holy Spirit, appearing only as a dove (Mt. 3:16, Mk. 1:10, Lk. 3:22, Jn. 1:32) or as tongues of fire (Acts 2:3), would even further challenge Michelangelo’s artistry. (I have a fuzzy memory of seeing a female statue of the Holy Spirit in a church in Europe several decades ago.)
In the New Testament, the Holy Spirit is compared to a wind, blowing here and there, outside of human control (Jn. 3:8), imparting special graces (Gal. 5:2), including extraordinary powers such as prophecy and healing (Acts 2:17, 1Cor. 12:8-9), and sometimes inspiring Jesus’ followers with what to say, especially in difficult circumstances and when challenged by authorities (Lk. 12:11).
The German Lutheran mystic, Jacob Boehme (1575-1624), author of The Three Principles of the Divine Essence  and The Threefold Life of Man , was engrossed for most of his life in the Doctrine of the Trinity. He wrote profusely about the various operations and reflections of Father, Son, and Holy Ghost throughout the universe, and also argued in opposition to Muslims and others who denied the Trinity.
The German philosopher, G.W.F. Hegel (1770-1831), fascinated with Boehme’s Trinitarian vision of the world, but critical of Boehme’s mystical enthusiasms as “making one’s head swim,” developed a more “scientific” philosophical worldview characterized by triads.
Hegel also joined Boehme in defending Trinitarian Christianity. Regarding the emergence of Deism during the French Revolution, Hegel writes that the Être suprême of Deism, extolled by Voltaire and other Lumières, was just a misty “Beyond” comparable to “the exhalation of a stale gas,” and then proffers his own “phenomenology” analyzing the ultimate emergence of Trinitarian “Revealed Religion.”
We often hear that the nuclear Christian family is a reflection of the Trinity, and it is. But of course there are myriads of other variegated reflections in our world, more even than the thousands supposed by great mystics like Boehme.