Is it possible to identify a fake wireless access point?

If you're using an unsecured network, quite simply, you don't. In that scenario, the only "proof" that you have of the network's identity is the service set identifier (SSID), or the "name" that is broadcast by the network. Unfortunately, anyone can configure a wireless network to have any SSID they'd like, so there is no real proof of identity in that case. When using an unsecured network, I strongly recommend configuring the host firewall to block all inbound connections. You should also use a VPN to encrypt all traffic between your computer and remote systems.

If you're looking for stronger proof of identity, you'll need to turn to secure wireless options. Wi-Fi Protected...

Access (WPA) provides a network connection when a shared secret key is verified. In a WPA scenario, a successful access attempt at least indicates that you're connecting to a network that is set up by someone who knew the shared secret. Unfortunately, if you're dealing with public hotspots, such verification generally isn't an option. Therefore, you'll need to assume the network is hostile. To ensure that you're practicing safe wireless networking, you should resort to the security measures I mentioned above.

More information:

Learn why public wireless networks present a raft of dangers.

Find out how mulitpots and 'evil twins' are bypassing enterprise Wi-Fi defenses.