What do you mean? Do you want to download a list of all street names in a certain regio?n If you go to the export tag, you can choose to export a region to a xml file (please try a little region first). when you've downloaded that file you can go to the part where the ways are (do a ctrl+f to "way id") and there you can see the streets. Some have no names, others have a name tag. I guess you can find a peace of software to filter out certain xml tags so you have only a list of the names.