I am afraid not although you can force the profile form to display on their first visit. You can also customise the message that appears at the top of the opening form. But nor force that change – sorry.

I would add that there are some registration plugins available for WordPress that, I believe, can be set to collect more information at registration time – like the Display Name. Many, if not most of these, play well with SP so it might be worth taking a look through the Wp plugins repository.