Yes, the standard way to do per-user or per-machine passwords on any IEEE 802.11 network is with IEEE 802.11i, which specifies the use of IEEE 802.1X (EAPoL, the Extensible Authentication Protocol over LANs). The Wi-Fi Alliance includes support for 802.11i as part of the WPA2 specification and certification program, and they included support for their own early snapshot of 802.11i as part of the WPA specification and certification program.
Some vendors call this mode "WPA2-Enterprise" or "WPA2 with 802.1X". Others call it just "WPA2", because they call the more common, consumer-ish, lower-security mode of WPA2 "WPA2-PSK" or "WPA2-Personal".
It looks like your TP-LINK TL-WR340G supports this and calls it WPA2 (as opposed to WPA2-PSK, which is what you're probably using right now). To use it, you may have to set up a RADIUS authentication server on your network, and point your TL-WR340G at that RADIUS server. Then you tell your RADIUS server about the usernames/passwords you want to allow onto your network. As an alternative to usernames and passwords, you can issue per-user certificates, and tell your RADIUS server which certificates to allow as valid credentials for joining the network.
Sites that want to do per-machine authentication usually use certificates. In this case the certificate's Subject Name is usually an identifier for the machine, not the name of a human.
Unfortunately, setting up 802.1X and RADIUS and whatever auth method you select tends to be a huge, huge pain. But it's possible, and it has been done, many companies use it every day, and I imagine that a few brave souls even use it on their home networks.