To be fair, they were walking through a frozen swamp.
I'm growing fond of the idea that James Bond is a cover identity specifically for 007 agents. MI6 recruits similar character profiles for this job. Orphans, hardened by life, with love for alcohol, women and their country. Then they give them the name James Bond to erase any ties to their true real life background.
It all started with an actual 007 agent named James Bond. Then he got killed in the line of duty, but MI6 thought it was a good idea to sort of keep the legend alive. So they recruited a similar type, and gave him the identity. And that practice continues to this day. Every now and then, when life gets in the way (like for example when he marries someone and his wife gets killed), they integrate that into the backstory for every future 007 agent. They even go so far as to change the date of the gravestones of the dead Bond parents.
So that's how he can walk around introducing himself as "Bond, James Bond" because the bad guys know the myth that once they kill him, a new Bond will appear.