Mr Ross does not give the same name twice in a row, so the six days
cannot include both Thursday and Friday. Therefore day 1 is a
Friday or a Saturday.
If day 1 is Saturday, then he says his real name on Thursday (day
6), which is therefore Bob. But he also says Bob on Tuesday (day 4)
the day when he definately lies, which is impossible, so day 1 must
be a Friday.
In this case his name is John, and day 7 is a Thursday, a day on
which he tells the truth. Therefore his answer on the seventh day
will also be John.
This problem is taken from the UKMT Mathematical Challenges.