Why is a call to RequestChat to the Chat API that contains custom fields not populating the custom fields on the chat workspace?

Environment: 

Chat API

Resolution:

Ensure you are referring to the custom fields by their formal name.  For example, here is an excerpt from the soap envelope:

...

    <RequestChat xmlns="urn:messages.enduser.chat.ws.rightnow.com/v1">
      <TransactionRequestData>
        <ClientRequestTime>2015-09-30T10:22:31.7156912-07:00</ClientRequestTime>
        <ClientTransactionID>0</ClientTransactionID>
        <SiteName>mysite__name</SiteName>
      </TransactionRequestData>
      <CustomFields dataType="STRING" name="c$chat_phone_no">
        <DataValue xmlns="urn:messages.common.chat.ws.rightnow.com/v1">
          <StringValue>123-456-7890</StringValue>
        </DataValue>
      </CustomFields>
      <CustomFields dataType="INTEGER" name="c$test">
        <DataValue xmlns="urn:messages.common.chat.ws.rightnow.com/v1">
          <IntegerValue>50</IntegerValue>
        </DataValue>
      </CustomFields>
      <CustomerInformation>

...

Note the naming convention (in bold) of the CustomFields "name" attribute for the custom fields.

For further information refer to Answer ID 5169: Technical Documentation and Sample Code.