If a company sent there emails from one domain; then chose to switch it to another domain would that now affect the successful delivery of emails from the company? Will there be deliverability issues?
How do I not have deliverability issues with the change?
The question is overbroad, so not possible to give a single answer.
If you set up DKIM properly (and SPF, only if you're using a branded sender domain) and are sending from the same, i.e. already-warmed, server IP, then a low-volume send after an overnight switch might be fine. But you should not start blasting overnight, start with your most engaged recipients as with a typical warming approach. And I'd advise making the domain switch itself clear in the Subject: line, even a loyal reader will be put off by a seemingly unsolicited email that doesn't explain that there was a rebrand.
There would not be issue but you need to work on IP warming first with most engaged customers and further you can go ahead with blasts.