How to add contents of a custom field to a taxonomy term list?

Replace the_field with get_field. The former echoes data without the need to explicitly call echo on the function name, the latter returns data, which is what you need when storing data against a variable for later use in your function. In your case, concatenating the first/last name prior to its output. That should fix your list.

Although the tags have been edited (thanks toscho), in case anyone is wondering, since it’s not clear in the OP, the function the_field is not to be confused with the native get_post_meta (and other) WordPress functions that handle retrieval of post meta data. Instead this particular function and it’s counterpart in get_field are part of the plugin “Advanced Custom Fields”