No, because each time you try to connect to your router it will require your computer to authenticate, not only that but the router's SSID is unique even if it's shared with another router in the same location. The reason lies not in the name but in the combination of the router's specific frequency, ip address, dns settings, ips predetermined proxy settings, channel, and unique network interface mac address the router is operating on/with.
@Aatif you are in error. The hacker would have to be closer to the user than the router itself, in order to create a hotspot that would have a stronger signal than the original router. This is because the PC can only show one when SSID's are exactly the same it chooses the router with the stronger signal. Meaning your's only if you are that close. Then you can DHCP3 to route the traffic to Internet from your PC.
So technically it's possible but highly improbable. There are other methods.