It should be able to, but that's just a guess. You have to find out how you can configure your modem. The important things:
* set a unique name for your wireless network (usually they come with default names set by the manufacturer or vendor). Setting a unique name would also help prevent, to some extent, others snooping or piggybacking on default network names
* disable "SSID" broadcast - this will ensure that your modem is not telling the whole world about its existence. This makes it a little more difficult for people to figure out that your network exists
* if you can, enable WPA encryption (don't use WEP, it's not good enough)
All the above settings can be done through a web browser - all that you need to do is connect your computer to the modem directly (using an Ethernet cable), visit the modem's address using a web browser (usually this address would be
http://192.168.1.1, but check your default gateway address if this doesn't work). You would also have to know what the administrator's username and password are for your modem - Verizon support should be able to help you with all (or most of) these.
Once you get your MacBook, go to 'System Preferences' and change the wireless networking settings to connect to your network (by specifying the exact network name you configured in the modem). If you have enabled encryption on the modem, then you have to enable encryption and provide the password to your Mac - this is also under the network settings.