Answer: Baby's Breath is a common name used for both some annual and perennial garden flowers (Gypsophila), and these are often seen for sale as cut flowers at the florists, too. Bridal Veil is sometimes used for a type of spirea, a very large shrub with white flowers in the spring.
There are numerous common names used for numerous houseplants but based on your description I think you have a trailing tropical plant called "Tahitian Bridal Veil" or Tripogandra multiflora. It may have been forced into bloom for sale time.
First of all, if it seems to be growing well it may simply be resting after its bloom cycle. General care would include a bright location, regular watering so the soil is evenly moist but not soggy and regular fertilizing with a water soluble fertilizer for houseplants.
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. When growth picks up again you may fertilize it lightly about once a month or so.
Always remove any dead or dried out stems. When this plant becomes rangy it is a good idea to trim it back pretty hard. Immediately after blooming is a good time to do this. If it has been in the same pot for a long time there is also a good chance it needs repotting. Good luck with your plant!
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