When you use tool functions, you can configure these waiting messages: https://docs.vapi.ai/tools-calling#adapting-the-payload-for-your-needs The one that says "One moment" is the

request-start

message.

"messages": [
        {
            "type": "request-start",
            "content": "Checking the weather forecast. Please wait..."
        },
        {
            "type": "request-complete",
            "content": "The weather in location is"
        },
        {
            "type": "request-failed",
            "content": "I couldn't get the weather information right now."
        },
        {
            "type": "request-response-delayed",
            "content": "It appears there is some delay in communication with the weather API.",
            "timingMilliseconds": 2000
        }
    ],

You can use your own or make it empty if you don't want the agent to say anything