How to get "Generated By" field in Webi?

In my WebI Report I would like to print the Author or the Last modified User name.

How can I obtain it?

Have a look at the manual Using functions, formulas and calculations in Web Intelligence, which contains a reference information regarding functions you'd need to retrieve this information. You can find the manuals for your specific version of BusinessObjects on help.sap.com.

The functions you're probably looking for are DocumentOwner() and DocumentAuthor().

Update:

While you can't retrieve the user's full name in Web Intelligence, there is a workaround, provided that

1. You're using third-party authentication (e.g. Windows AD)
2. You're able to pull the full name from that source into the CMC

If so, you can use User Attribute Management to define a new user attribute in the CMC and then create a new dimension in your (UNX) universe which uses the @Variable to get in the new user attribute value.

From the IDT manual (paragraph 18.3.6 About @Variable, version BI 4.1 SP5):

To reference a User Attribute, specify the internal name for the at­ tribute as it is defined in the CMC. @Variable returns the value of the attribute for the current user. For example, the User Attribute MYCOUNTRY contains the value of the country of each user in the CMC. Specify the attribute's internal name surrounded by single quotes:

@Variable('SI_MYCOUNTRY')

The attribute’s internal name is defined when the attribute is cre­ ated in the CMC

User Attribute Management is described in the Administrator Guide, paragraph 6.2.17 Managing attributes for system users (version BI 4.1 SP5).