The collective wisdom is that you can not install a vCenter without a DNS Server in your environment. This is not true. Of course it is not an ideal solution to install without DNS but it is possible. What you lose though is the ability to update the vCenter directly and you can also not do a lookup on it but that is to be expected.
I would recommend to install the vCenter if possible with a DNS server but maybe you have a small lab environment or an air gapped small cluster you want to manage with vCenter without setting up a DNS server in it first. Or you just want to spin up a small vCenter in an isolated environment to try out some things on it. I was trying to do this and have found that there are some tricks that need to be followed if you want to do this:
Install vCenter
The install of the vCenter itself is like you would do it normal until you reach step 9. Configure network settings.
Here you want to keep the FQDN and DNS entry empty.
The vCenter install should now go through like normal until you reach Stage 2. For some reason here the next button on the second step where you configure NTP and SSH is greyed out, no matter what you configure in here:
The solution here is to go directly to the IP of the vCenter on port 5480 so for example in my case it's https://10.24.0.33:5480. Here you are able to continue.
The next window asks you to put in the network information. Here, however, you are not able to continue if you do not put in a System Name and a DNS Server as these fields are required. The solution is to put in "localhost" as a system name and "127.0.0.1" as the DNS server. This way the vCenter is able to resolve itself among the entry in the host file it has.
After that the installation will go through just fine and your vCenter will install and start. Of course you can not add any hosts by DNS Name etc. as everything needs to be done by IP. However if you decide to start up a DNS server at a later stage you can just add it in the VAMI (port 5480) and change the hostname of the vCenter.