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?
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.
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.