“David Hilbert” doesn’t sound like a very German name to me. Is it a typical German name? Were his parents Anglophiles or did he get his name from somewhere else?
Well, “David” is not a very frequent name in German, but the name exists, and it’s spelled exactly the same as in English. My impression is that the name has become more popular in the past few years than it used to, which might be due to anglophone influence (this influence, incidentally, has brought a wave of Kevins and Dennises to Germany, names that had been practically nonexistent before in German). After all, it’s a biblical name, so I’m pretty sure it has been around in German for centuries. But as said, it’s not overly frequent (I know only one David personally).
The family name Hilbert certainly looks English, but the suffix -bert is very common in German, both in forenames and family names. So I’d say that the name of the mathematician is indeed a “typically German” name; it’s coincidence that at the same time it looks “typically English.” Keep in mind that German and English are closely related languages.
Hilbert’s family belonged to a somewhat fundamentaist protestant sect that preferred biblical names, of which David is a prime example. As for Hilbert, the only reason it sounds like it might be English is that English has absorbed a great many Germanic names. It is, after all, a Germanic language.
Hilbert was from Koenigsberg (of the bridges fame) which was totally demolished during the war and has been taken over by the Russians and is now called Kaliningrad. It is still part of Russia, although separated from the main component by the Baltic states.
It’s the same in Sweden. The most common name, given to boys this year is William, looking at the list I find that Kevin is in 30th place and Liam is 31. There’s also Oliver (19), Elliot (46), Vincent (76) and Charlie (96). The girls are less prone to be named with English sounding names, the highest ranked is Nelly (39) followed by Molly (58) and Melissa (98). Some are borderline. I think Nicole is French, originally, but seeing how little influence French culture and pop culture has in Sweden, my guess is still that it came from the UK or US. Same for Michelle.
As opposed to Germany, this has been going on since the 50’s with the celbriity *du jour * inspiring parents. Back then it was Gary, Steve, Glenn and some sad sack got named Sven-Elvis by his parents. That’s just wrong.
Meanwhile, my cousins here in Canada, children of my Swedish uncle, got names like Eric, Ingrid, and Linda. 
Though the next generation has names like Jason, David, Becky, and Stephen.
Ah, thanks Schnitte.