what kind of naming server do you mean? The one which is holding remote references of Java objects - like a JNDI server or the RMI registry - or a DNS server for host name lookups?
Anyway in both cases you simply have to query the name server for the information you want to know. If you want to know for example if there's an existing DNS entry for the full qualified host name of host "foo.example.com" you have to query the DNS server for a corresponding so called A-record for this host. You can do this in an own program or with one of a lot of available command line tools in UNIX/Linux for example. It's similar for JNDI. You have to use a JNDI client to query the JNDI server.
A DNS server is usually standalone so there's no problem in this situation. For JNDI there's often a JNDI server used which is embedded in an application server. This way you won't have luck if your application server is down.
Sorry Meir, but unfortunately I've got no experience with Corba
But I could imagine it's pretty much the same as with JNDI and DNS. If it's a standalone server you can simply query it for the information you want to check. If it's part of an application server it will be obviously down when your app server is down so you can only check it if there's some kind of persistent data store for the data.