We are using AMS for indexing and encoding video blobs. AMS is creating as top level containers to store the assets in the Storage account.
We also have other top level containers such as images, videos, pdfs etc to store blobs which get stored as \images\<filename>, \videos\<filename>
Storage account is now cluttered with assets from AMS. Is there a way to set a container name to AMS so the assets get generated inside the provided container instead of root level (by pre-appending the container name to the assetfile).
No. You have no control over container names for Assets. They have to be unique, that's why there is also GUID associated with the container name.
By the way I wouldn't share a storage account with media services. Media Services should have its own (if not more than one) storage account.