Verses 1 to 8 depict a vision John was given, and he writes it down as he saw it. First, he gives his location. Note that the previous vision has ended (regarding the dragon). Now John finds himself standing upon the sand of the sea (the sea-shore) and out of this sea arises a monstrous beast. He describes the appearance of this symbolic beast and what happens to one of its wounded heads. He sees, in vision, people of the world worshipping this beast, then the beast being given a mouth to speak boastful and blasphemous things, and being given power that will continue for 42 symbolic months. It starts to blaspheme, and to war against God's people on earth while controlling all peoples and nations.
All of those things indicate on-going action with a beastly system that clearly links in with the vision of beasts that Daniel saw. There Daniel was given to see from the political power of Babylon through to the power of Rome, on the world scene. But John's vision of beasts had this difference: his were composite and went way into the future, from the time of Rome up till Christ's return. It is the way the book of the Revelation moves from John's time through till the still-future return of Christ that accounts for changes in tenses.
As you point out, previous visions about the dragon trying to kill the woman's man-child etc were past tense. That makes sense given how that event speaks of Satan's failed attempt to destroy the Christ-child more than 90 years before John got that vision.
Further, they continue in the past tense (and also present tense) because from Christ's arrival on Earth right through to his still-future return, Satan's beastly political systems have kept trying to destroy Christ's followers on Earth. In every generation, there have been various, and continuing, fulfillment of the different visions. And with each century the events get worse and worse. Same with the plagues poured out from heaven down on to an increasingly godless world. And, likewise, the horsemen of chapter 6 have been riding forth continually, until this very day.
However, the build-up of events show a climax that is to be reached very soon before Jesus suddenly returns. And this, I suggest, is the reason for verse 8 being future tense. There are penultimate events yet due to happen; seven last plagues; three final woes. Then the last trump to announce the start of the Day of Resurrection and Judgment. So in chapter 13: things were beginning to happen in John's generation, they would continue into the next century, and the third, and right on till today, but even as of today, we still await the revelation of those names written in the book of life of the Lamb to be revealed. That won't happen until the last trump, which is still future.
It is amazingly appropriate how tenses switch throughout the book of the Revelation. It is not arbitrary. Christians of every generation since John have been provided with intelligence as to what will happen, and what they are to expect. It has been given to enable Christians to endure until Christ's sudden return, to make sure they are not deceived into worshiping this satanic beast out of the sea, brought about by the other beast out of the earth. Those beasts manifest throughout the centuries, but at the last gasp, they will pull out their final deception, shortly before Christ returns. It is for this that the Revelation was given - to let God's people know what happens to them, and what will yet happen, for nobody knows when Christ will spectacularly appear, and Christians are already being targeted, to deceive them and to stop their witness for Christ.
Post Script with another example of changing tenses within one verse in Revelation: Rev. 5:6 - Present tense, "And I beheld..." This is part of an on-going vision where more is revealed about the throne of God. Past tense, "...stood a Lamb as it had been slain..." The slaying of Jesus, the Lamb of God, had taken place some 60 years previously, a once-for-all-time event. Present tense again - the Lamb is standing, alive, taking action. Verse 9 continues this fluctuation in tenses, The Lamb is worthy to take the book and open the seals because he was slain and had redeemed people (now depicted as being in heaven), then verse 10 switches to future tense with those redeemed people looking forward to when they will reign on the (new) earth.
This is a clear example of Revelation switching from present, to past, then to future tense, and it seems self-evident in this case as to why. Similar careful examination of the text in question should show this also.
