What stops the server from using a different domain name?
In general, nothing. It's possible in the case of a court order that the domain registrars would be under an order to not allow the site owner to register a new domain, and it does cost some money in any case, but in general it's a simple business transaction (you have to provide some personal information but not a lot). Then, once the new domain name is published, you point it at the server; setting up the DNS records can take some effort (especially if you want to e.g. use email with the domain name directly) but it's not hard. If you want to serve TLS traffic (typically HTTPS) for the domain, you'll need a TLS certificate and want to get it from a trusted certificate authority; setting that up can be a little effort but not terribly much (and these days it's possible for free).
It might take a little while before the new DNS entry is available everywhere, but probably only minutes. It might take a bit longer before the site is indexed under the new name by search engines, but still probably only hours.
What stops one from accessing their server directly using IP address like in the example above for google?
Possibly nothing, but in practice people don't usually go for it.
- IP addresses are hard to remember, annoying to type, and unfamiliar to most people. This is one of the primary motivators behind the domain name system, after all.
- When making an HTTPS connection (such as TLS), the client (browser) will expect the server's name (in the URL bar) to match the name given in the certificate. If using an IP, they won't match; no public CA will issue a certificate for an IP address. This will, at minimum, cause a scary-looking browser security warning. It also prevents using some advanced security measures, such as HTTP Strict Transport Security.
- Depending on how the site is hosted, it might be impossible to reach it by IP alone. Many sites are co-hosted on a shared IP address, and the browser tells the server which one it wants via domain name. Google doesn't have this problem, of course; they outright own a large chunk of IP addresses, and assume anybody connecting to one of them is trying to reach Google. But smaller sites, and those with minimal budgets, may require the browser to identify the site it is trying to reach by name, either using SNI (for HTTPS) or just in the
Host: HTTP request header (for plain-text, or after the TLS connection is established).
Finally, it's worth considering that the site might not still be online to connect to. It depends on the details of the court order, how it was executed, where the site was hosted, and more, but in theory the courts can order a hosting company to take down a server / block a customer's account, or an ISP to cut off a customer (which would prevent even hosting on your own hardware, at least until you got a different ISP). I don't know if any of that applies here, but generally speaking, unless the order is specific to the domain name rather then the site (e.g. because it's subject to a trademark dispute or was illegally seized)