Following on from the blog post on how to produce horizontal dot charts this blog shows you how to label the dots rather than use labels on the Y axis.
Before hiding the horizontal bar elements select them and use the right mouse button / add data labels (note that in later versions you can how use data call outs if you want that format)
Then select the data labels and format them to show the Category name rather than the value. In later versions of Excel you can also chose to display a different range of cells so that you don't have to be constrained the the category name.
Then hide the bars as before and then hide the left hand Y axis in the same way that you previously hid the right hand Y axis.
Now you have dots next to the labels. If any of the conflict with each other you can select an individual label and chose to display it in a different place or even drag it away and have it linked by a call out line (though this can add another level of complexity when maintaining the chart).