Why do we say in English Police Department instead of Department of Police?
They mean the same thing and Police Department is more efficient (fewer words/syllables).
Same reason we say New York City and not City of New York. However, there may be legal reasons to say the latter in the example of
The City of Oklahoma City
which sounds redundant, but is the legal entity for Oklahoma City.
If I am talking about the departments that the City Council or Mayor oversees, I might say, "We oversee the Departments of Fire, Police, Social services and so on." We could also say, "She oversees the Department of Police and City Services."
"The Police Department is one of many city services we control from the Mayor's Office."
"The Department of Police is headed by the Police Commissioner, who reports directly to the Mayor."
SO I think the Police Department refers to the police specifically. The Department of Police is referring to one department among other departments.
(I've been wrong before!)