there will be no changes to the domains themselves, or their content.
Unless I am missing something here, why would changing your registered name ownership of a domain name affect your SERPs?
The only thing I can think of is:
I'im planning to change the Company name
You won't rank for your new company name since the original will still be shown however that's assuming you have your company contact details listed now.
I'm planning to change the Company name in which my domains are registered
No reason why it should have any effect on the SERPS (for terms other than the company names).
But if any of the domains are .co.uk's, remember that a change of name of the registered owner is the same as a transfer to a new owner: involves costs and archaic paperwork, and the old owner needs to still be in existence to transfer them.
I have 57 .co.uk domains, but since the company name is just a contact name i am hoping the change doesn't involve any other red tape.
Have a look at the Nominet site (under "transfer"). What counts is whether the name in the "Registrant" field changes. If it does, that can be considered a transfer but they do list exceptions (such as if you are retaining the same company registration number). Daft, but that's the way they work.