“It is best to define personality when used of the Divine Being or God very carefully and not by human standards. God was not made in the image of man… God is not a deified man. Only God the Father has a perfect personality. When one possesses the attributes and qualities of personality, then personality may be unquestionably predicted of such a being.” So yes, God does have a personality.
All the names of God imply personality. When Moses asked God who should I say is sending me, God said, “say that, ‘I Am’, has sent you.” The central idea of this name is both existence and personality. As you search the Scriptures you will find that God grieves, gets angry, can be jealous, loves and even hates. In addition, He cares, provides, disciplines, forgives, heals, listens and much more.
Finally, personality exists where there is intelligence, mind, will, reason, individuality, self-consciousness and self determination or free will. So it is fair to say that both God and man have personalities in order that they can have communion and personal relationships. Christianity is unique in that a human being can have an intimate personal relationship with an infinite, eternal and omniscient Divine Being, God, who created all that exists in the heavens and on the earth. That’s Amazing!