This question is a little silly, but sometimes it's tough to figure out how to name things correctly. The conversion will parse a config file into XML and vice versa. I want to call the program MyCompany.Config2Xml, but the program also needs to be able to "Xml2Config".
General term seems like it would be format convertor, or transformatter (by analogy with transcoder). In terms of the specific names you discuss, I think I'd go with ConfigConvertor.
In keeping with SqlDataReader, TextReader, XmlReader etc I'd just call it ConfigReader and ConfigWriter.
Or, you could just go the serialization approach and then not have to worry about naming conventions.
Rather than ConfigParser as proposed by jeffamaphone (+1 for nice username), make it a verb:
parse-config
This makes it read nicely in scripts:
if ! parse-config < config-file > config.xml; then exit 1 fi
I think it helps a lot to think about the verbs (methods) you intend to use with the class and the role the class plays in the application.
In other words if you envision the operation to be {class}.Get() or {class}.Load() then ConfigParser might be a good choice.
If on the other hand you have a corresponding {Class}.Set() or {class}.Save() operation then something like ConfigManager would be a better choice, particularly if the class will be used to isolate the application from the persistence of its configuration.
If the role of the class is nothing more than part of a standalone application or a step in a longer running process then I would would lean more towards class and method pairs that are more like Convert.ToXml() Convert.ToConfig() or Translate.FromXml() Translate.FromConfig().