Using the catalog, it's possible to share a dataset to a single member of the organization.
To do this, go a dataset you would like to share (you need to have the proper permissions to share the dataset - data managers and admins may, but data viewers may not).
Select the share icon form the dataset action bar. This will open a share popover which will show you all the active shares on the dataset. If you want to create a new share, select the "+ New share" button.
In the Share details section, select "member" from the available options. This will open a form where you can select any member of the organization (or let you invite someone). You may also provide a message.
Next, select their access level. You may also provide any advanced share options, if necessary. Click "Share" to complete the process. You may then review this share at any time by reopening the share popover.