How come Mr. Braun doesn't remember Suzuha? In episode 16 Suzuha goes back in time. Unlike what happens when they send a D-Mail or time-leap, this doesn't cause the divergence ratio to shift — which in turn means all lab members still remember her, since she was just there.

However, after that, Mr. Braun goes to the lab to give Okabe Rintarou a letter from Suzuha, saying:


  It's a letter from someone who once took care of me.


Does he not remember her working for him as a part-timer? That would be weird, given everyone else in the lab appears to still remember her.  

Or is the name change — from Amane Suzuha to Hashida Suzu — along with the age difference enough to make him not realize they're the same person?
As you pointed out, yes it is because of the name change. But let's look at the timeline of events after Suzuha  travels back to 1975 without changing the divergence ratio. 


1975: Suzuha Amane (19 years old) arrives in Tokyo but suffers amnesia.
1978: Yugo Tennouji (aka Mr. Braun) is born.
1999: Suzuha Amane (43 years old) remembers the events from before the time travel. In this time she helped Yugo Tennouji (aka Mr. Braun), who was 21 years old at that time, as Hashida Suzu. Suzuha Amane/Hashida Suzu suicides. 
2010: The 19 years old Suzuha Amane arrives in Tokyo and applies as a part-time worker at Yugo Tennouji (aka Mr. Braun) CRT store. Yugo Tennouji (aka Mr. Braun) is 32 years old in 2010.


So he only knew a 43 year-old friendly lady with the name Hashida Suzu who helped him 11 years before the events of D-Mail. It's not absurd that he doesn't connect her with a 19 year-old Suzuha Amane.

Source: Suzuha Amane Wiki, Yugo Tennouji Wiki