I have a lot of app services on alot of different storage accounts. I would like to consolidate some. Can you move function apps and app services to new storage accounts? I have not found anything in the admin UI.
An App Service doesn't run on a storage account, it connects to a storage account. Which means you can simply switch connection strings. You should, however, think about migrating data as well.
Azure Functions have a storage account associated with them (although these, too, are connected to with a connection string) because of managing triggers and dashboarding functionality.
More information here: Storage considerations for Azure Functions.
When creating a function app, you must create or link to a general-purpose Azure Storage account that supports Blob, Queue, and Table storage. This is because Functions relies on Azure Storage for operations such as managing triggers and logging function executions.