Send String to a function inside a class
Try with the new version, U8g2lib.

With that version, you can write code like this:

String t1 = "Grow";
String t2 = "Room";
u8g2.firstPage();
do {
  u8g2.setFont(u8g2_font_logisoso24_tf);
  u8g2.drawStr(32, 24, t1.c_str());
  u8g2.drawStr(32, 60, t2.c_str());
} while(u8g2.nextPage());