Is it possible to link my old Skype name to my newer O365 account? Right now it is as if I have two Skype accounts.
The old Skype name is firstlastname (as an example)
My O365 New account and associated Skype name is email@example.com
This is going to depend on some specifics of your situation. You might be able to if both are consumer accounts. If the Office365 account is a work or education account then you probably won’t be able to.
If you search for “merge Microsoft accounts” you can find some tutorials that will walk you through it if they are account types that can be merged.