I can simply get full users collection and sort on client side. But that not efficient at all, as soon as users base grows up I'll got performance issue on client side.

I can separate incoming string into array of all possible variants of chars:

fun shredNameIntoPiecesForSearchingInDatabase(name: String): List<String> {
    val lcName = name.lowercase()
    val shreddedName = mutableListOf<String>()

    for (i in lcName.indices) {
        var item = lcName[i].toString()
        shreddedName.add(item)
        for (j in i+1..lcName.lastIndex) {
            item += lcName[j].toString()
            shreddedName.add(item)
        }
    }

    return shreddedName   // for "Name" it will return [n, na, nam, name, a, am, ame, m, me, e]
}

This one work well and accurate but I have no idea how bad is it to store that big array in firestore as a field (even if user name will rarely exceed 40 chars, it result 741 combinations).
This method can be more efficient if just replace all combinations with combinations from 1st char to last on each word + limit user name to specific length (now with string.length == 40 it will return 38 combinations). but I still wonder how bad it gonna be for database?

I can use separated queries and merge them after.

Or I also can use thirdparty libs for firestore.

Mb there better solution for that?