First Name & Last Name VS Given Name & Family Name

Why facebook and google use First Name & Last Name when some countries have family name first followed by their given name ?

Why not just use Family Name and Given Name, and I think this is more clear. But seeing this, I'm not sure anymore. Is it so common that people will automatically put their name correctly? If Google and Facebook use it, I think it is standard now, but I want to know why first name & last name is better and more commonly used than given name & family name.

I'm building a website that will be used internationally, I want my users can interact with other people from different countries, and I'm concerned about some countries that have culture of calling person by their given name without their permission is considered rude.

UPDATE answering Serg's comment

Actually I'm asking about more general user experience, not for specific project. It's for my consideration for future projects that could have totally different subject than my current project.

For now, I'm working on open source apps that will be available world wide. Using this apps, user (company owners, admin, etc) can store data of employees, customers, suppliers, etc. I think first name and last name will be crucial when e.g company owner/sales department sending email / calling their customer.