Apparently, they are aware of git issues now. Reply to my case
Our R&D team investigated the issue, and it seems that the Git integration causes the issue.
When new files are added during the recording, there is the setting that will automatically add them to the repository. So, let's disable that option and check if this improves the situation. To do that, go to "Tools | Options | Source Control | Bind new items to SCC automatically." Then, disable the "Bind new items to SCC automatically" option and try running TestComplete again.
Turning this option off solved the slow name mapping. I am unclear what features I am losing. If I don't use the source control ui through Test Complete, I am guessing not much.
True, disabling the feature means they don't get things automatically bound... however, you can still MANUALLY bind items to SCC via the right-click context menu. It's an extra step, but not critical. I expect that the SmartBear folks will be working on figuring it out so we SHOULD get a patch sometime in the future.