@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.
- Migrate exactly as the site is now. Same url structure, images, text and in/out bound links.
- Setup 301 redirect permanent with the old domain directing to the new domain.
- Run a PR campaign on authority PR news sites about the migration.
- Make sure to use both links in the PR article.
- 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!