As Thomas already said, you need a unique ID for each node to create the node and to describe the connecting edges between the correct nodes. A good way to do this is to use numbers "1", "2", "3",. In other columns, you can have label texts or any other data. Since this data isn't used to identify nodes, any number of nodes, or even all nodes, can have the same data values and names.
Note that there is no special 'conversion' for the input data. The created diagram will contain exactly one node for each unique node ID and one edge for each row in the edge list data range.
If I understand your example graph correctly, one of the problematic nodes is 'Update Display'. Instead of a node with 4 incoming and four outgoing edges, you want to have four nodes with one incoming and one outgoing edge instead. To achieve this, the Excel file must contain four rows with different IDs but the same text in the 'Name' column cells. Please see this Excel file for the correct data for this part of your diagram: http://yed.yworks.com/support/qa/?qa=blob&qa_blobid=8677134676228643102
The corresponding Excel import settings are these: http://yed.yworks.com/support/qa/?qa=blob&qa_blobid=7982193948023418365
On the 'Presentation' tab, set the 'Label Text' of nodes to 'Name' to see the node names.