I found that the tiles are generated under the Mercator projection in openstreetmap(here).
And in the wiki page,they provide the Derivation of tile names which is used to Calculate the covered tiles name at a certain point(lng,lat).
So I wonder if there is any difference if the tiles are generated in another projection like EPSG:4490?
If the projection isn't spherical Mercator, or if there is a different tile naming system, then you can't make the same assumptions about tile names.
In general, you'd have to do a normal projection operation to find the coordinates in the projected space that correspond to the longitude/latitude of interest, then apply the rules that apply to a particular tile naming system.
The first part can be done fairly easily with a tool like proj.4.
The second part probably can't be solved in a general way. There may not even be tiles that correspond to any given longitude / latitude pair, depending on how tiles are named (e.g. for a projection based on a UTM zone, you probably don't have tiles for most of the world, because that projection is only valid for that UTM zone).
Sometimes tiles in other projections are tilted by few degrees in relation to original projection after reprojection of that tile. If that is the case you can't use simple renaming process since they won't fit together and you'll propably get some overlaps and gaps.
