DNS searching with wildcards?

You can get a full list of entries in a zone with a zone transfer; you'd need to allow this for authorized systems in your DNS server.

Once that's done, you can run the transfer and grep the result:

dig axfr localdomain.com | grep -i miller

A name server will not, by design, let you search a zone or query what zones it is authoritative for. Beyond the obvious reason of reducing attack vectors (you can't make a HTTP/1.1 request to a host if you don't know its name), there is a very good reason for this: a zone can contain wildcards itself, so asking for every host in such a zone is like dividing by zero.

If you operate the name server whose records you want to search, you can do a zone transfer to a local name server and search the records directly. You will still need to parse the text records in whatever format they are transferred in, as a local name server will not respond any differently.

You can only ask a DNS-Server if it has a specific record. So, no there will be no such tool for DNS.

Edit

Zonetransfer is of course a possibility if it is available.