In Yahoo! Mail you can create disposable email addresses, but these are not automatic. You have to set these up ahead of time.
Settings (gear icon) → Security → Disposable Addresses
When you set it up you will be asked to choose a base name and as many as 500 different keywords.
The format of the disposable email address will be like this:
In the above, examplebase is your basename (and different to your actual Yahoo! username), the customword one of the 500 keywords available to you.
These custom disposable addresses therefore will not reveal your true Yahoo! email address.
Another thing with the subaddressing is that emails must be sent to a previously created keyword. You cannot receive emails to a disposable email address you haven't set up, and you cannot send to the address if you remove the keyword.
For example, removing the keyword from the disposable example email address from before:
Sending to that address will go nowhere.