Once you remove the background from an image, you can reuse it. However, the approach you take will vary depending on the intended use of the image.
Google: How to correctly find transparent images (no background)
Choose one of the three formats on the screen: GIF, PNG, or JPEG.
GIF: Graphics Interface Format is the original format with transparency support for the web. The problem with GIF is that it reduces the color palette to no more than 256 colors, which causes color shifting, posterization or banding of colors, and distortion in images with many colors, such as photographs. If the physical dimensions of the image are small or if you are posting the image on a social media site, you should consider using a GIF image. Another disadvantage of GIF is that it only supports 1-bit transparency. This means that every pixel in your image is either completely transparent or non-transparent.
PNG: Portable Network Graphics images overcome many of the limitations of GIF and are a better option for transparent images. The file format supports high color and partial transparency using alpha channels. Transparent PNG files have been supported since Internet Explorer 7 and are now supported in all popular web browsers, so it is safe to use PNG today unless you know a large portion of your audience is using very old hardware and software. PNG images are also commonly seen on mobile devices.