Will a valid, non-expired US Visa work on a cancelled passport?

Question

I have a valid non-expired B1/B2 US visa on a cancelled passport.

I had to cancel the old passport because my last name was abbreviated as "T". It is abbreviated in the US visa as well.

I got my new passport with a corrected, non-abbreviated version of my last name as "Thevaril".

My new passport also mentions my old passport number.

Will I be allowed boarding/entry to the US if I carry both passports?

If not, then will I have to reapply for a new visa or can my visa be transferred to the new passport as it has not expired yet?

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UPDATE:

I applied for B1/B2, filled the questionnaire and was eligible for interview-waiver. All I had to do was:

1. Schedule an appointment for drop-in.
2. Carry DS-160, appointment letter, 2 photographs, along with my old and new passports.
3. Inform the VAC staff at the counter that I need to update my surname on my Visa.

That's it. I received a new Visa on my new passport in 1.5 weeks. The new Visa had new expiry starting from the date of issue of new Visa.

Answer 1

See the State Department page About Visas - The Basics:

If your name has legally changed through marriage, divorce, or a court ordered name change, you will need to obtain a new passport. Once you have a new passport, the Department of State recommends that you apply for a new U.S. visa to make it easier for you to travel to and from the United States.

Now this is not quite your situation, but it does imply that you can travel to the US with a valid visa in an old passport where the name does not match your valid passport. They don't recommend it, however.

The problem you're likely to have the most trouble with isn't the immigration inspector at the border but the airline agent issuing your boarding pass. I would consider calling the airline to ask about that, but don't be surprised if they refuse to give a clear answer. Airlines typically won't do so because they do not want to be bound by an answer that may have been given without access to all the facts.

In the end this comes down to your risk tolerance: are you prepared for the possibility of struggling with the ground staff? Are you prepared for the possibility of losing that struggle and not being allowed to board? How likely do you think those outcomes are?

I think you're likely to be able to board, but I'm not at all confident about that. If you are able to board, I'm far more confident that you won't have much trouble at the immigration inspection.

If not, then will I have to reapply for a new visa or can my visa be transferred to the new passport as it has not expired yet?

The US doesn't transfer visas. You can certainly apply for a new visa if you want more peace of mind.