I can think of a few decent options for this bracket layout. For a simplistic approach, you could simply label them First Round, Second Round, Third Round... Final and leave it at that. Not very elegant, but serves the purpose of providing a label.
Another option could be to base the loser's bracket labels on the round from the winner's bracket they are coming from.
Qualifiers Elimination Round
Eights Elimination Round
Loser's Quarters Round
Quarters Elimination Round
Loser's Semi-Final Round
Semi-Final Elimination Round
Grand Final Elimination Round
Alternatively, you could shuffle these around and use the term Play-in.
Qualifiers Elimination Round
Eights Play-in Round
Eights Elimination Round
Quarters Play-in Round
Quarters Elimination Round
Semi-Final Elimination Round
Grand Final Elimination Round
I still see an issue with the "Grand Final" round, as the winner may have already beaten the loser and to win, the loser will have to beat the winner twice, but that's not really relevant to the question at hand, I suppose.