I understand I can sort by clicking on the “Name” column label.  I just want to adjust the setting so that it automatically sorts by name.

@MARCORAC 
For BoxWeb, sorting in All Files will apply to all folders and files under it.

Please follow the steps below to check if the default sorting is by "Name":

■ Steps:
1. Click "All Files" from the left-hand menu.
2. Click the "Name" column.

Sorting from All Files does not reset the default. If you share the folder, the recipient of the link will see the folders in Date Updated order (which seems to be a default within Box generally). 

Yes, by default, a Shared Link to a Box folder presents your content in order of most recently Updated. 

You can Customize Shared Link Content Ordering instead where shared links to a Box folder can be automatically sorted by a different column (e.g. Name or Size), when opened.

To sort by a different column:

1. Click your Shared Link
2. Click the name of the column you want sorted, and you'll notice the shared link in the URL bar changes.

You can use this new URL as your shared link, and each time you access this link, the content is sorted as you specified.