Looks like no "name" parameter in graph.update() is counted as "name": "", not as "do not change graph name" (as it should be, in my opinion), because after sending something like:

{
"jsonrpc": "2.0",
"params": {
"yaxismax": 496,
"gitems": [

{ "itemid": "106935", "color": "ee1764" }

],
"graphid": "6779"
},
"method": "graph.update",
"auth": "69376a316c220bbdeeadf90bd4958b59",
"id": 9
}

I've got
{
"jsonrpc": "2.0",
"id": 9,
"error":

{ "message": "Invalid params.", "code": -32602, "data": "Graph with name \"\" already exists." }

}

If I'll add "name" field in my graph.update() request — all works fine.