You can get a list of changes for a given build id via the REST API, like this:
http://<yourTCServer>/httpAuth/app/rest/changes?build=id:<buildId>
The response from that request will include one or more "change" entries, depending on how many commits were included in the build. Each of those entries will look something like this (assuming response is formatted as XML; you can get JSON if you prefer):
<change id="####" version="<commit id>" href="/httpAuth/app/rest/changes/id:####" />
You can then follow the returned href to get the details of each change, which includes a tag for the related user looking like this:
<user username="<some TC username>" name="<some TC user's full name>" ... />
The root "change" element will also include the git username, but if you've got all of your users setup correctly within TC so that there is an association between the git users and TC users, you'll get the "user" element I showed above and it will contain more info.