Sounds like this kind?
Dragon Wing Begonia (Begonia Dragon Wingยฎ Red)
If you click onto the page you should see an "add this plant to your list" button. If that is your plant, you could click the button to add it to your plant list, which this site will store for you for free. No need to try to remember. : + )
It's no problem to trim them. You can use the trimmings to make more plants. Make your cut right above a leaf, for 2 reasons. First, you don't want it to look like it has "sticks" at the tips, and second is in case you want to use the trimmings, you'll have the longest possible length of stem to stick into soil, all the way until the bottom leaf is touching the soil.
