First of all, congratulations!
In my experience, depending on your SAML set-up, you may have the "best-case" scenario where your name change is reflected with the change in your single sign-on, with the caveat that your username will not change (this cannot be changed).
However, if your SAML creates a new user with a new username reflecting your name change you can migrate your content over as an administrator of ArcGIS Online and just remove your previous account from the organisation. You will also have to consider rejoining any group you were initially a part of.
I hope this helps!
~Just trying to fix things~