Accessing usernames
If User owns data is used for embedding, then while authenticating, the username is accessible in the code.
Or, even if using App owns data, if you authenticate your users while accessing your portal, then you can get the username while authentication.
Below is an example on JS
oCommon.authContext.getCachedUser();
Below is an example in C#
HttpContext.Current.User.Identity.Name;
Filtering in the embedded report
Further, by using filtering capabilities of Power BI embedding, the report can be filtered on the username value fetched during authentication.
Avoid flickering
You will be able to apply the filter after the report embeds, if you use powerbi.embed().
Instead use the concept of phased embedding, where before the report even renders, you can apply the filter. So apply the filters after load() and before render(). This will avoid the flicker that you may have with filtering after powerbi.embed().