Does phobos (D's standard library) contain "endsWith" for string type?

I need a function to test if a string ends with some suffix. I can use 'lastIndexOf' for this task, but I wonder if there is a standard phobos' function?

Yes, it does. std.algorithm.endsWith works with strings as well as other arrays and ranges. Example:

void main()
{
    import std.algorithm.searching, std.stdio;
    auto s = "Sunday";
    auto b = s.endsWith("ay");
    writeln(b); // true
}