Make contact firstname and lastname mandatory

Because this is a standard field, I don't think there's a lot you can do with this with respect to making them required fields.

A workaround would be to create a validation rule that checks whether or not both FirstName and LastName are filled.

The condition might be something like the following:

ISBLANK(FirstName) || ISBLANK(LastName)

This would return true if FirstName or LastName is blank.

I suggest create a validation rule for first name.

Make first name required using validation rule