@dodo123 I would seriously consider not doing it.
But, if you must, follow these steps to help retain most of the SEO of the previous domain.

1. Migrate exactly as the site is now. Same url structure, images, text and in/out bound links.
2. Setup 301 redirect permanent with the old domain directing to the new domain.
3. Run a PR campaign on authority PR news sites about the migration.
4. Make sure to use both links in the PR article.
5. You can also create a new, but similiar site to the old one onto the new domain for 3 to 6 months. Linking from the original site to the new site in a safe SEO way. Once you start seeing the new domain ranking in Google SERPS, you can then do steps 1 - 4.

It can take a year or longer to regain that ranking and "convince" Google that your still the same awesome website, but with updated brand.

A PR article or two on the rebranding can help make the conection.

If the old brand has a Wikipedia page, update that account with the rebrand information/history and new updated link.

LMK what you decide and your results. Good luck!