Depends on whether they have any rights in the U.S. You wrote that "have it trademarked in the UK and US", which means that they do.
In that case, if your goods/services are similar, you cannot use that name or any name that is "confusingly similar". Merely adding a geographical designation to the end would be confusingly similar, so you would be out of luck.
If they have not registered in the US, have not made any US sales, and have not done any US marketing, then you might be able to get away with it. You should talk with a trademark attorney first, because I guarantee you that the amount you spend on an up-front consultation will be much less than the amount you spend on a lawsuit and settlement if you missed something.