Goal: Within a contact, the name field is concatenated in the user view and I would like to add custom fields to this concatenation. Currently, appears this is not possible, though possible I am missing something.
Background: Within Salesforce it appears that the name field is a set of three fields: Prefix, First, Last; documentation say it's just the First, Last - though at least my instance appears to be the Prefix, First, Last.
Also, it appears that this summer, that Salesforce will be introducing the new default fields to make this: Prefix, First, Middle, Last, Suffix.
"I'm pleased to announce that we will be offering a sneak peek of Middle Name and Suffix on Leads, Contacts, Person Accounts and Users in our upcoming Summer release. More details to follow on how you can get access to this functionality for your organization." Blake Markham - Salesforce, Product Manager
Name
field is one of the "special" system fields. You don't have control over that. You might want to create a custom field as @brovasi mentioned and concatenate any fields you want, then use your custom "Name" field...