From lambda answer, I have made something closer to the requirements.
boolean imageCreated = false;
Bitmap bmp = null;
Marker currentLocationMarker;
private void doSomeCustomizationForMarker(LatLng currentLocation) {
if (!imageCreated) {
imageCreated = true;
Bitmap.Config conf = Bitmap.Config.ARGB_8888;
bmp = Bitmap.createBitmap(400, 400, conf);
Canvas canvas1 = new Canvas(bmp);
Paint color = new Paint();
color.setTextSize(30);
color.setColor(Color.WHITE);
BitmapFactory.Options opt = new BitmapFactory.Options();
opt.inMutable = true;
Bitmap imageBitmap=BitmapFactory.decodeResource(getResources(),
R.drawable.messi,opt);
Bitmap resized = Bitmap.createScaledBitmap(imageBitmap, 320, 320, true);
canvas1.drawBitmap(resized, 40, 40, color);
canvas1.drawText("Le Messi", 30, 40, color);
currentLocationMarker = mMap.addMarker(new MarkerOptions().position(currentLocation)
.icon(BitmapDescriptorFactory.fromBitmap(bmp))
// Specifies the anchor to be at a particular point in the marker image.
.anchor(0.5f, 1));
} else {
currentLocationMarker.setPosition(currentLocation);
}
}