Straßennamen ändern - change the name of a street

Short answer:

There are many ways to edit the map data. See the Beginner's Guide for an introduction, particularly chapter 1.3 (Editing maps).

Longer answer:

The easiest way to get started is to use the online editor (Potlatch):

• Go to http://www.openstreetmap.org/
• click "Edit"
• create an account and log in
• navigate to the street whose name you want to change, and click it (it should become highlighted)
• in the detail pane on the left, change the name
• click "Save" (top), enter a comment like "corrected name of Orchard Road"

Things to note:

• Longer streets may consist of several segments (called "ways" in OSM). Each way has a separate name; if all ways are part of one street, all these names must be identical. In that case, you will have to click and edit all the ways/segments individually, or you must use Ctrl-click to select all the ways to edit them in one go (see comment below for details).
• If, on the other hand, a part of one way has a different street name than the rest, you will have to split this way. See the question Changing the status of a separate section of a road.