You are using an after business rule to update current. That beaks rule no. 1 of Business rules: whenever the current record is to be updated, it must be done using a before business rule.
Rule no. 2 being: whenever a different record than the current one needs to be updated, it must be done using an after business rule.
The other issue is the RegExp itself; it should be:
/^From:\s*(.+)$/mi
Another issue is that you are using the name directly to set the field. You need to fetch the user's sys_id and use that to set the value of the field:
GetIDValue('sys_user', )
Something like:
// Script to extract sender name from RITM description and set as requested for
// Get RITM description
var description = '' + current.description;
// Use regular expression to extract name from "From" field
var senderName = description.match(/^From:\s*(.+)$/mi);
// Set extracted name as requested for
current.requested_for = GetIDValue('sys_user', senderName[1]);
Of course the code should check that the value returned by GetIDValue is not null and only set the requested for if it is not. This is also a very fragile solution as the slightest mistype, even an additional or missing space in the name and it will not work.
