@Rick Spears , Thanks for the great question. Apologies for the delayed response on this!
In Azure Media Services Explorer you can name an asset when you upload it.
In the upload dialog click on Asset creation options and choose the name of the asset. Just to highlight that the name of the asset must be unique with Media Services. Additionally, when you encode an asset you can go to the Output asset tab and choose the asset name there.
Media Services has limited search functionality. The asset name is meant to be a key for you to provide an exact value when you need an asset. We recommend using a database paired with Media Services where you can track filenames, which owns the asset, long descriptions or other metadata as well as the Media Services asset name.
Hope this helps! Thanks for your patience.