I am creating a personal page for each employee in our company and need to know how to make each employee searchable by first, last or both names. Can someone please help?

You might want to do this using the Active Social or Smart Social modules.

Not sure what you mean...

Those sets of modules will let you create a personal profile page with other features like a wall, photo albums, etc. for people.

You could also use Effority's User Directory.

You could also use OWS, the Form and List module, or Tressleworks' SGSV module.