If I deleted a graph from the Studio UI can I create a new graph with the same name?
No, you cannot reuse the graph ID for a different graph.
Apollo’s internal tooling retains all the graph characteristics/history/etc. that they had before being deleted.
And to be precise, the graph “ID” is what we are talking about. We also have a concept of graph “name” which is an arbitrary string which doesn’t have to be unique over any domain.