how to add/edit city name?

Cities are tagged with place=* either on a node (simplest method) or on an area (if you have better info). Either find the existing node/area and add the name tag on it, or create the node/area yourself.

You do not need to download the whole city to do this :

• If you're going for the node, just download the city center where the node should be. Using potlach or using josm's "continuous download" plugin might help if you are searching.
• If you're going for the area, just download one corner of it. Ways are always downloaded as a unit, so if part of the way exists inside your download area, the full way will get downloaded.
• It's possible that the area already exists as a relation. In that case, tag the relation itself. You can optionally download all members of the relation by right-clicking on the relation in josm's sidebar.
• If you know that no node/area exist yet, you could even create and upload it without first downloading any data. Places are "immaterial" anyway and shouldn't share nodes with other map features (unless two city-areas are touching).

Please install the mirrored_download plugin in JOSM. You can then download from a mirror server instead of the main server. The mirror servers allow for much larger areas than the main server.