When it’s time to publish your ETD, you will upload in two places: the University of Miami Scholarly Repository and the ProQuest Dissertations and Theses database. The Scholarly Repository provides a publicly available, searchable, full text repository of UM theses and dissertations. The ProQuest Dissertations and Theses database contains dissertations and theses from universities around the world and is subscribed to by thousands of libraries.
You do not need to register with the Copyright Office in order to retain copyright in your work. Copyright is automatic once a work is in fixed form.
For some, there may be benefits to registering your work. You are required to have registered your work if you were to try to sue for infringement of copyright. Registration also allows you to sue for statuary damages (rather than just actual). However, this is often more of a concern to authors of creative works rather than scholarly works.
When you deposit your dissertation with ProQuest, you will be given an opportunity to register your copyright for a fee. The University of Miami does not require that you register your dissertation with the Copyright Office. If you would like to register your copyright at a later date, you can do that by registering directly with the Copyright Office.
See the UM Libraries’ page on copyright here.