Guillaume would be lovely

What a lovely idea!

I just checked that his last name is Marie. Let's keep fingers crossed that this would explain Mary

There a lot of royals with Marie. Catholics tend to use Mary or Marie in their names, even the males. Gui and all his siblings have Marie, and oddly enough, all but Gui have Gui as a last name. (Guilliame Jean Joseph Marie, Felix Leopold Marie Guilliame, Louis Xavier Marie Guilliame, Alexandra Josephine Teresa Charlotte Marie Wilhemine).
Princess Astrid and Prince Lorenz's children all have it
Prince Amadeo Marie
Princess Maria Laura
Prince Joachim Karl-Maria
Princess Louisa Maria
Princess Laetetia Maria
Philipe and Mathilde's children
Princess Elizabeth Therese Marie Helene
Prince Gabriel Baudouin Charles Marie
Prince Emanuel Leopold Guilliame Francoise Marie
Princess Eleanor Fabiola Victoria Anne Marie
Closer to home, Princess Birgitta of Sweden's children
Désirée Margarethe Victoria Louise Sibylla Katharina Maria (all three of her children also have Maria)
Carl Christian Friedrich Johannes Meinrad Maria Hubertus Edmund Prinz von Hohenzollern (his one son has Maria)
Hubertus Gustav Adolf Veit Georg Meinrad Maria Alexander (his one son died at 4 days old and didn't have it)
I don't think Gui is close enough to Vik and Dan IMO to be used yet. If Mary has anything to do with a godparent I guess either as the wife of one of her godfather's (Freddles being an extremely likely godfather) or because of Philippe/Mathilde. The couple named Vik as godmother to Eleanor who has Vik as a middle name. If they didn't choose to use one as a godparent to Estelle, maybe they chose Mary as a middle name in honor. Or it could be an odd honor to both of their sisters, though in Anna's case, it should have been Maria. Madeleine's name comes from Magdalena (Mary Magdalen) and Anna is Anna Maria.
They do seem close whenever they attend events together. Though I would love to see him as a godfather, I still don't think so.
Almost every member (except Princess Margaretha) of the family has Guillaume/Wilhelmine in their names, not only all of the kids of Henri and Maria Teresa.
Grand Duke Jean: Jean Benoît
Guillaume Robert Antoine Louis Marie Adolphe Marc d'Aviano
Grand Duke Henri: Henri Albert Gabriel Félix Marie
GuillaumePrincess Marie-Astrid: Marie-Astrid Liliane Charlotte Léopoldine
Wilhelmine Ingeborg Antoinette Élisabeth Anne Alberte
Prince Jean: Jean Félix Marie
GuillaumePrince Guillaume (obviously

):
Guillaume Marie Louis Christian
And all of Guillaume's children: Paul Louis Jean Marie
Guillaume, Léopold
Guillaume Marie Joseph, Charlotte
Wilhelmine Maria da Gloria and Jean André
Guillaume Marie Gabriel Marc d'Aviano
In fact all of Luxembourg's Grand Dukes had Guillaume/Wilhelm or Wilhelmine among their names and as you can see above every person who has succession rights to the throne also has. The Hereditary Grand Duke will become Guillaume V. when he ascends to the throne.