Display labels based on language selection

If you are using pre-rendered raster tiles, you are stuck with whatever your provider chose to show.

If you are using vector tiles then it may be possible to configure them to display another label depending on who has produced them.

In terms of raw data if you're creating your own tiles, the name of an object is normally recorded in the name tag in the local language or according to local convention if there are multiple local languages. Names in specific languages are recorded in separate tags identified by the ISO language code e.g. name:en. These tags are not always present so you will need some form of fallback in case the English name is not recorded anywhere. See the multilingual names page on the wiki for more information.

There are several projects that use not the local language for a region, but display all labels (if existent) in English, French, etc. Some of them also use transcribing of local names. I don't know of an example showing only Russian labels worldwide, but for a selection of European languages you'll find examples through https://www.osmap.info for raster tiles.

See https://wiki.openstreetmap.org/wiki/Map_internationalization for more info and a list of vector and raster tiles with non-local labeling.