Client is in a legal dispute over their business name, wants to use a different "temporary" domain for now and possibly change it back once the matter has been resolved. What are the main SEO concerns, and how best to tackle?

I have a doctor client who has a region-related business name "[city] [service they provide]", and that name space can get somewhat cluttered when there are several competitors. TLDR is that there is a legal dispute between him and another doctor in the area, and while the dispute is the dental board has requested for him to use a different domain name. Most likely we will use a new one that is centered around his actual name since he essentially *is* the business. It is also worth mentioning that there is a good chance they will eventually rule for him to be able to keep the business name and domain name. I have already bought the new domain name but I'm wondering, from an SEO perspective, what would be the best way to handle this without losing too much SEO strength? The website is in WordPress and it should be easy for me to migrate it over to the new website, although I may have to do some search + replace and also use a different logo but that's not a huge issue. I believe the strategy is to use as few references to the old name and domain as possible. I've seen that apparently we can let Google know that we are changing the domain name. Also we can do some 301 redirects of some sort. How much can we expect these changes to hurt his SEO, especially considering the domain name had relevant keywords in it while his name and domain do not. Also, what generally is the best way to do this migration? Any help would be greatly appreciated. It's really unfortunate that he even has to do this since he's been using the same business name for ~40 years but apparently he never actually registered the business name (dba). I want to try my best to make sure it doesn't hurt his business too much.