Hello Sue,
Welcome to Infopathdev Forums.
Create a field in the form which populates the person's name when the form is signed and promote this field into sharepoint form library when publishing. You can put an OnAfterChange on this field so that when ever the new signature is added the field is updated.
I hope this will help you.
Kalyan G Reddy
Infopath MVP 2007 and 2008