No, sorry. If you open your Kindle and see the name of G-d on your screen, even by accident, you have to bury it.
OK, I'm just kidding. But in all seriousness, I think the absurdity of the alternative already gives you the answer. The real question is: why? And for a good halachic justification, I shall leave the field open to others more learned than I... :)
EDIT: Some people have taken me to task on this answer and downvoted me for it, and I can really understand why. According to the pure bounds of truth, one has to be intellectually honest and accept the halacha, whatever it may be.
OTOH, I think it is very important to realize that this world was specifically not created with the pure middas hadin (attribute of judgment), but rather by and admixture of emes (truth) and shalom (peace). The role of a posek (Rabbi who makes halachic rulings) is not just to find the truth, but also to find a peaceable solution to the big picture. See, for example, the attitude of Rabbi Chaim of Volozhin in the case of the Aguna of Vilna, quoted from here:
Regarding the case of the Aguna of Vilna I see you are
leaning toward stringency. You feel
the woman should not remarry.
The reason you are leaning this way is
because you are not here. You do not
hear the crying of this woman nor do
you see her tears. If I would be where
you are I too would be stringent, but
I am here. I will rule leniently for
her. May G-d save me from mistakes.
(Rav Chaim of Volozhin in a letter to
one of the great poskim of his
generation. Quoted in Chut HaMeshulash
Now maybe a Kindle is not as big a loss as a woman's ability to remarry, but I assure you that if ever this question came to discussion in front of a posek, his first, knee-jerk reaction would be, "Let's find a way to permit this, so that this poor guy doesn't have to lose his Kindle."
Agreed, I don't have the big shoulders of a posek like R' Chaim of Volozhin to make such a ruling, but I would be hugely shocked if nobody could find a solid heter (leniency) to permit you to keep on using your Kindle after a shem Hashem appeared on its display.