A. What is the name of the horse that won the race?
B. What was the name of the horse that won the race?
Both are acceptable, but the first makes more sense if the event was recent, while the second makes more sense if the event was not recent. If, for example, The Preakness was yesterday and I was inquiring about the race, I would use the first one (is).
A. Alexander Bell is the man who invented the telephone.
B. Alexander Bell was the man who invented the telephone.
Since Alexander Bell is dead, only the second one makes sense.
A. Margaret Thatcher is the first woman prime minister in the UK.
A. Margaret Thatcher was the first woman prime minister in the UK.
Margaret Thatcher is not the prime minister, so only the second one makes sense. (You can only use is if she currently holds the office.)
A. Bill Clinton is a former President of the US.
B. Bill Clinton was a former President of the US.
You have touched on a pet peeve of mine. Bill Clinton cannot stop being a former president until he dies or unless he somehow gets reelected to the office. In the first instance he would be a dead president, and in the second instance he would be president (heaven forbid!). (The word former denotes the status of someone.) Obviously, I think the second one is wrong.
A. This is the knife which was used to kill the victim.
B. This was the knife which was used to kill the victim.
Only the first one makes sense. The knife's status is unchangeable. (I'd argue with that use of the word victim, but perhaps that's another discussion.)
>A. Alexander Bell is the man who invented the telephone.
>B. Alexander Bell was the man who invented the telephone.
>A is strange as he's dead
Are 'is' and 'was' both acceptable if Alexander Bell is alive?
No, because you are talking about a status that is unchangeable. If you use was that at the very least creates possible ambiguity, suggesting to some that he is dead. (If he really is dead, there of course is no ambiguity.) (Despite the objection I stated, some will find was perfectly acceptable in that situation.)