Hello Kathleen!
Yes, Alexa does recognize multiple voices. When setting up your Echo, you go through a training process where you say the phrases on your smart phone's screen aloud so that it can learn from the way you speak.
You can always go back into the Alexa app, select settings, and Voice Training.
Any time you, or anyone around you, activates Alexa using your preselected activation word (selectable in the Alexa app under Settings, Alexa Devices, (your device name), and 'Wake Word') - it learns. The Echo keeps track of every request, along with a voice recording of the request, for learning purposes. If, at any time, you would like to remove those recordings, you can do so within the Alexa app under settings, Alexa Devices, and History - this is also where you can view more information on what Amazon uses and why, as well as other privacy information. Keeping this voice history, along with selecting the requests within the app and letting it know whether the Echo did what you wanted it to, helps it to better understand requests.
In the past, Alexa has been activated by late night hosts commenting about Amazon Echo, causing reactions from Amazon Echo devices in the vicinity of the TV. You can always disable the microphones by pressing the microphone button on top of the Echo, and you can change your wake word to Alexa, Amazon, or Echo, which is definitely helpful if you have someone in your household named Alexa.