The thing is, the Japanese language has very few sounds compared to most languages, so their loan words have to be forced into the system of sounds they have.
For «hamburger» specifically, they don’t have any of the vowel sounds in the English word. They also lack the rhotic «r» sound, or really any «r» sound at all (edit: that is similar to the languages they loan words from). Their «a» sound is an open sound as in «say aah», so they just ended up using a long version of it to approximate the «ur» and «er» sounds (which are really similar in American English!).
That’s pretty close, though!
The thing is, the Japanese language has very few sounds compared to most languages, so their loan words have to be forced into the system of sounds they have.
For «hamburger» specifically, they don’t have any of the vowel sounds in the English word. They also lack the rhotic «r» sound, or really any «r» sound at all (edit: that is similar to the languages they loan words from). Their «a» sound is an open sound as in «say aah», so they just ended up using a long version of it to approximate the «ur» and «er» sounds (which are really similar in American English!).
My favorite one is “Urubarin”, for Wolverine! Pretty close, yet so far.