That's not the most random way to select people. Here's how you should do it:
Arrange the names alphabetically, then number them 01-XX. Then get your hands on a random numbers table. (If you're in college, anybody in a Statistics class will have one)
Then, choose a line off the top of your head and go through it, looking at the numbers in pairs. (If over 100 people sign up, do it in 3s, and label them 001-XXX.) Those whose numbers appear on the table will be chosen, and those who are not will not be.
This is the most widely accepted way of randomly choosing individuals from a group, and it is a Simple Random Sample, or an SRS.
In order to raise someone's odds, assign them two or more numbers.
This is superior to the random number generator in excel because computers can never be truly random— they are only pseudo-random. A completely randomized random numbers table will do the job more truthfully, or you can measure atmospheric noise or flip coins if you'd like.