All Catholics and other trinitarians believe that Father, Son, and Holy Spirit are three distinct persons that share one divine nature (aka consubstantial). This was established in the 4th century during the Council of Nicea.
To beleive that Christ was talking to himself would require holding to the Sabellianist heresy of Christ, the Father, and Holy Spirit being different manifestations of the same God in one person. Catholics also explicitly reject adoptionist heresies that believe Christ was born human and later became divine. All three persons of God have existed for all eternity; none were created or existed before the other. These facts were all established during the first 7 councils and are fundamental to Christianity. It is why so many heresies had to be rooted out and the various Christilogical creeds formed.
You likely cannot tell what my avatar is, but it is often call the Scutum Fidei or Shield of the Trinity. The three outer circles contain the three persons of the Trinity and the inner circle is God. The lines between the outer circles say “non est” (is not) where as those from the person of the Trinity to the circle of God say “est” (is). This encompasses orthodox Christian understanding of the nature of God as expressed in the Athanasian Creed.