Answer: Based on your description I think you have a "Tahitian Bridal Veil" or Tripogandra multiflora. Your plant might be suffering a bit from a number of things. First of all, it may be in shock simply from being moved. This plant might also prefer more light than it is currently receiving since it is a sun lover adn likes a bright location.
In winter when growth slows, it is best to cut back on the watering somewhat; check to see if the top layer of soil is dry before you water. When you do, make sure the water soaks the rootball and isn't just running straight out between the pot and the soil.
You did the right thing to remove any dead or dried out stems. When this plant becomes rangy it is a good idea to trim it back in any case, so certainly you did it no harm.
If it has been in the same pot for a long time there is also a good chance it needs repotting. When growth picks up again you may fertilize it lightly about once a month or so. Good luck with your plant!
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