If you really want to use the '-regex' option of find, then you can do it like this:
find . -regextype posix-extended -regex '.*/hosts\.txt|.*/ipaddress\.txt'
Watch out for the special meaning of '.' in filenames, you'll have to escape it with '\'
Also remember that -regex works on the full path, not just the filename.
colucix' -name version is probably easier though.