I'm not intimately familiar with MS PKI, but it was a question that came up in a discussion for an issue a coworker is having. When you input the request fields manually on a PKI server, the cert generated has an automatic name given to it. When requested via a pasted CSR, it's just called cert-new. Is there a field in the CSR that can control this?
From what I've seen, no - usually the certificate signing requests (CSR or PKCS10) are all about what the cert should look like, or what the cert will be describing. How it's stored when it's retrieved is a matter of the software you are using to request and retrieve the certificate.
I'm not sure quite what you are trying to do, but it's possible to rewrite the client side of the request if you have the time and money to spend - I seem to remember than the Microsoft CA and/or a fronting IIS server can be configured to listen for CSRs and respond appropriately - with that capability, you'd have the option of storing the output any way you like.