"Honor of" just refers to the applicator name for the bunch.
Alternate names: order of, glory of, blessing of, fate of

There are three suggestions, but they can be separated and used for other events if they don't quite fit June.
Since June is known to have bases with bold texture, keep in mind these bases were designed to meet that mark.

Lapis

Alternative names: Amun, Apis, Lazuli
A hue shift to be more blue instead of teal is possible, I might add that version later
 

 

Alternate Lapis

 

 

Tomb

Alternative names: Crypt, Serket, Montu
 

 

Sekhmet

Honestly I'm not so sure this one fits June, it could also be a nice groupie base under Delta