The MIT license is very permissive; you are allowed to release your own work under a different license if it was based on something released under the MIT license.
See also this answer on Software Engineering SE and the plain English explanation of the MIT license (link also provided in the linked answer). As indicated in the plain English explanation, you are allowed to sublicense the work:
You may incorporate the work into something that has a more restrictive license.
The only condition of the MIT license is that you include the MIT license text and any copyright notices from the original author.
Any files in your fork that already existed in
hugo-theme-dream should have a copyright line with the year of creation and the original author's name. Per MIT terms, you have to leave these in.
Any files that you created yourself after forking and thus are 100% written by you do not need to include any such attribution, since there was no copyright notice in those files to begin with and you wrote them yourself. However, if you copy, move, or otherwise transfer code/text that you didn't write from a file written by the original author, you should also copy over the copyright line (or at least acknowledge that that piece of code/text was written by the original author).
You seem to have already done this, but for the record: since other people might want to use the original work under the MIT license (e.g. if you make your fork available under something more restrictive), it would nice to include a link to the original repository so other people can easily find it.
TL;DR: any copyright lines from the original author need to be left there. You should include a copy of the MIT license in the repository and acknowledge that your work is based on someone else's work, which is available under the MIT license. You can apply your own license to your fork.