Hopefully this will get what you're after.
For this example, I'm using the following folder structure.

See full flow below. I'll go into each of the actions.

When a file is created (properties only) triggers when a new file is uploaded into the Staging folder. Your folder structure will likely be different to this.

Name and Type are Compose actions that retrieve the Name and Type using the following expressions. Note that this assumes the file name structure you mentioned. "YYYY.MM.DD_Name_Type"
//Name
split(triggerOutputs()?['body/{Name}'], '_')[1]
//Type
split(triggerOutputs()?['body/{Name}'], '_')[2]

Create new folder Name and Create new folder Type try to create the folders. If they already exist the it won't do anything, but if they don't exist they will be created. Note that they use the outputs from Name and Type.

Move file uses the Identifier from the Trigger and Full Path from Create new folder Type.

After uploading a file into the Staging folder, it should be moved into the Name/Type folder.