I don’t think Persits PDF will help here. The file is generated by Persits but then moved to Azure blob storage. Any client can only request the file as per it’s actual full path. The only way to change this is by overriding the headers and adding something like this.
filename: Content-Disposition: attachment; filename=mycompany_invoice_111.pdf
I will leave this open and if it becomes a more popular request we can look into this a bit more.