I guess John 14 goes into a good bit of detail.
Jesus is in the Father, because the Father is omnipresent, and contains everything.
The Father is in Jesus, because He is YHWH of hosts.
Jesus was the first complete fulfillment of "host."
The OT heroes were hosts, but came short of complete.
"So God created man in his own image, in the image of God created he him; male and female created he them."
Male represents God, Female represents mankind.
In-dweller and container.
"And Adam said, This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man."
Like a created mankind came out of an omnipresent God
"Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh."
Like Jesus became one with the Father. (The man and his wife don't merge into a single body, but they beget a representation of that merger in their children)
"...and thy desire shall be to thy husband, and he shall rule over thee."
Like our desire is to God, and He rules over us.
"Thorns also and thistles shall it bring forth to thee"
To reflect the same way the world brings thorns and thistles and grieves God since the fall.
So He is not the Father proper, but rather one (the first) physical representation of Him.
As far as the name goes, the question in proverbs 30 is a double asking of the question of a shared name.
"God will save", represented literally in "Jesus" and poetically in "YHWH", which is the sound of your next unprovoked breath, which also saves you. But those are fairly simple explanations of a very deep name meaning.
Jesus says to worship and pray to (ask) the Father in His name, so I rarely "address Jesus", and when I do it is in comment, not usually in request.