Hi Matthew,
I'm really glad to hear that you're finding the Incremental Spatial Autocorrelation tool useful! Actually, we are working really hard on some improvements right now and the tool is going to be CORE in ArcGIS with the 10.1 release, which we're really excited about! One of the improvements that we're making relates to what you're asking about as far as the name of the graphs. In the 10.1 version of the tool we're making the output a PDF, for which you will choose the name and location. This should help with the issue of overwriting graphs. For now though, what I've been doing is renaming the graph once it is created, so that on the next run of the tool the new graph wont overwrite the old one (since it wont have the same name). Sorry for the inconvenience there!
As far as the performance issue, I need a little more information to understand what's going on and hopefully get to the bottom of it. What beginning distance and distance increment are you using? How does that compare to the full extent of your data? Also, how many distance bands are you testing? A screenshot of the tool right before you run it will help me get a picture of exactly what you're doing.
Also, are you seeing this performance issue only when you run the tool from inside of a model? If so, what exactly does the model do? A screenshot of the model would help as well.
Lastly, is is possible to share your data? The best way for us to figure out what's going on is to try to repro it, ideally with your data. If not possible, the more specific you can be about the data (ie the geographic extent, the type of values in your analysis field, etc., the better.
Hopefully we'll be able to get to the bottom of this!
Lauren Rosenshein
Geoprocessing Product Engineer