It's about time to update (and improve) my old Gmail - Customize header line. Especially when Google have updated the interface.
I think the screen-shots explains it all.

As in my obsolete style there are several ways to hide the username address. select your own preference:
a. Make the username address text faint and hard to spot form afar.
b. Cross out the username address. The enabled preference (to see address use mouse to select address text).
c. Cross out the username address using the background color (to see address use mouse to select address text).
d. Completely remove the username address.

P.S
Best viewed when using Google 8pt v2.2 by PhiloHippus@userstyles, but it's also OK on it's own.