That Jesus is the speaker (through His chosen representative) in the seven letters in Revelation is evident by comparing the letters. Note especially:
The greeting to the church in Smyrna:
These things saith the first and the last, which was dead, and is
alive; (Revelation 2:8)
The greeting to the church in Thyatira:
These things saith the Son of God, (Revelation 2:18)
Also compare Revelation 3:3 to Matthew 24:42-44 - it is Jesus who will come as a thief in the night. Other examples from the 7 letters could be cited; the speaker is Jesus.
References to the Father
The speaker makes several references to the Father in the letters. For example:
He that overcometh, the same shall be clothed in white raiment; and I
will not blot out his name out of the book of life, but I will confess
his name before my Father, and before his angels. (Revelation 3:5)
To him that overcometh will I grant to sit with me in my throne, even
as I also overcame, and am set down with my Father in his throne.
These passages clearly reference more than one person.
Jesus refers to the Father as "my God"
Not only does He do so in Revelation, Jesus most definitely refers to the Father as "my God" in the Gospel of John:
Jesus saith unto her, Touch me not; for I am not yet ascended to my
Father: but go to my brethren, and say unto them, I ascend unto my
Father, and your Father; and to my God, and your God. (John 20:17)
This implies that the Father is someone else, somewhere else.
The speaker is Jesus, and as He does throughout the New Testament, He shows deference in this passage to His Father and God.
Are the speaker and his God two separate persons? Yes