You can't do this with out of the box API/Classes.
This is usually done using a Feature Services, and placing the features in a graphic Layer. There are also some advances done in decreasing the overheads of Vectors in web Mapping by using UTF grid. However, I haven't seen the implementation of UTFgrid with the ArcGIS JSAPI.
So now you need to enable the recognition of features from images (i.e. from your Map Service). It is definitely possible, but not easy. I have explained how this can be done in this Answer. But making it so that you can recognize additional Attributes like Park Name, is not going to be easy, since there are potentially thousands of park names.
To Summarize, it is possible, but not trivial.