How do I change query param name inside the HTTP::query object in my iRule?

If I may add, you can extend that to test for specific param names. Example:

when HTTP_REQUEST {
    if { [string tolower [HTTP::query]] contains "qc=" } {
        HTTP::query "qd=[URI::query ?[HTTP::query] qc]"
    }
}

You could also change it with a string map:

when HTTP_REQUEST {
    if { string tolower [HTTP::query]] contains "qc=" } {
        HTTP::query [string map -nocase {"qc=" "qd="} [HTTP::query]]
    }
}