I see a lot of people make "mill" Decks around
Oona, Queen of the Fae (who shares colors with Gyruda), but they have more of an "
exile everything" theme than a "claim cards from opposing Graveyards" theme like Gyruda would have. That being said I'm sure a lot of the cards in the one would also work in the other, if that helps at all.
EDIT: A lot of Liliana and Sorin planeswalkers are pretty good at taking stuff away from opponents' Graveyards, although many Sorins have white so they wouldn't work with this Commander.
DOUBLE EDIT: If you wanted to try making a Deck with white blink that meets Gyruda's Companion conditions, you could start with a Commander like
Sharuum the Hegemon (for ETB triggers) or
Varina, Lich Queen (for theming and acceleration). That probably isn't the best approach but it could still be an option.
TRIPLE EDIT: Consulting my
close-to-complete Planeswalker list tells me that most Sorins and many Lilianas have even CMC, and also that fewer Sorins have white than I previously remembered. Finding an Esper Commander with even CMC to use Gyruda as a Companion actually lets you use a lot of them.
I apologize for all of the editing. Gyruda is one of my all-time favorite Magic cards for reasons that relate to a card game other than Magic.
QUADRUPLE EDIT, LOL: I didn't intend to actually post the list, but instead to link it indirectly like other forums would have, whoops. Please don't ban me over it.
QUINTUPLE EDIT, WOW:
Deadeye Navigator has blink but is mono-blue, and blue also has some cards that return stuff to hand (but then you'd have to hardcast it again, hmm). With the Esper angle you gain access to
Venser, the Sojourner, but he doesn't have even CMC...it's going to be even more difficult to push this than I initially thought. I really want this to work somehow.
EDIT THE SIXTH: I just discovered you've been brewing for a while. Here I am rambling pointlessly over an obviously inferior approach...ignore me please. I'm going to try it my way, I don't care if it's worse. I just won't take over your topic with my nonsense anymore.