SP 2010-2013 upgrade users issue

Hi to all

I’ve performed an upgrade from SP 2010 to 2013; in particular, the SP 2010 WA was using windows authentication, so for migration I have converted it to claims authentication via powershell before upgrading to 2013.

I’m having some issue on user profiles:

under People and Groups, on the user lists, some user are displayed as DOMAIN\user, other as “Surname Name”.

Also, if I click on user to get details, for some users the destination page is the “standard”    “page _layouts/15/userdisp.aspx….”, for others is “/my/Person.aspx?accountname=…” even if I didn’t confiugured my sites in the UPS

My questions are:

• Why I have 2 different users notation?
• Is there a way to have all users as “Surname Name”?
• How can I get rid of the redirection to the non-existent my site page for the users pointing to it?

Thanks in advance for any suggestion

Regards