In the last Harry Potter book we are told Kreacher's tale, consisting mostly of Kreacher describing how Voldemort, upon Regulus' offer, used him to test the defenses of the Horcrux in the cave (Slytherin's locket):
“So Kreacher went to the Dark Lord. The Dark Lord did not tell Kreacher what they were to do, but took Kreacher with him to a cave beside the sea. And beyond the cave there was a cavern, and in the cavern was a great black lake...”
...
“And then the Dark Lord sailed away, leaving Kreacher on the island....”
Obviously Voldemort did not care about Kreacher. After Kreacher drank the potion, he left him there, probably to become Inferi. He didn't worry about him. To support this let's quote Hermione:
“Of course, Voldemort would have considered the ways of house-elves far beneath his notice, just like all the purebloods who treat them like animals.... It would never have occurred to him that they might have magic that he didn’t.”
Harry Potter and the Deathly Hallows, ch. 10, Kreacher's Tale, pages 194-6
But let's go back into the fifth book, the Order of the Phoenix. After Sirius' sad death, we discover through a dialogue Dumbledore has with Harry. They discuss that was Kreacher himself who passed crucial information about the relationship between Sirius and Harry to Voldemort through the Malfoys and Bellatrix:
But he gave Narcissa information of the sort that is very valuable to Voldemort, yet must have seemed much too trivial for Sirius to think of banning him from repeating it.
...
Like the fact that you were coming to regard Sirius as a mixture of father and brother. Voldemort knew already, of course, that Sirius was in the Order, that you knew where he was — but Kreacher’s information made him realize that the one person whom you would go to any lengths to rescue was Sirius Black.
And, this is important, Voldemort instructed Kreacher to mislead Harry if he tries to contact Sirius:
“The Malfoys — undoubtedly on Voldemort’s instructions — had told him he must find a way of keeping Sirius out of the way once you had seen the vision of Sirius being tortured. Then, if you decided to check whether Sirius was at home or not, Kreacher would be able to pretend he was not. Kreacher injured Buckbeak the hippogriff yester- day, and at the moment when you made your appearance in the fire, Sirius was upstairs trying to tend to him.”
Harry Potter and the Order of the Phoenix, ch. 37, The Lost Prophecy, page 831
The last quote states that the Malfoys gave the order to Kreacher, so Kreacher was probably not speaking directly to Voldemort at any time before the battle at the Ministry, but Voldemort must have known about Kreacher being at the Malfoys. I can not imagine Malfoys talking about some elf, or somebody at the Headquarters of OoP. Yet he still seems to be okay with it.
Question is: how come Voldemort was not suspicious over why Kreacher is alive and happily reappearing at the Malfoys after all these years? Even if he did not worry about Kreacher, he might worry about the safety of the locket. We don't have any proof of him not checking the Horcrux, but I really don't think he did it - at least from how he behaves in the last book when he hears about the Trio breaking in & out of Gringott's.
Update as a response to first two comments
After rereading the part from OoTP I came to this: if we put aside Kreacher's name, what could the elf have told Narcissa? He could not tell her where he comes from (meaning the house):
You see, Kreacher was not able to betray us totally. He is not Secret-Keeper for the Order, he could not give the Malfoys our whereabouts or tell them any of the Order’s confidential plans that he had been forbidden to reveal.
Personally I think that the only other option is that she recognized him (even after more than fifteen years) as her aunt's/uncle's (don't know the relation) house elf.
But what would they tell to Voldemort? I understand, fifteen years is a long time. But that was not an ordinary thing Kreacher's done.
About the Voldemort would have considered the ways of house-elves far beneath his notice argument. This is an argument for Voldemort not hesitating to leave Kreacher in the cave, not worrying about him having the possibility to escape and tell anybody. Applying it here would meant something like:
Well, the elf survived and knows about the Horcrux (even if he didn't realize what it was, he could still tell it to somebody), but it is just a house-elf. No threat.
I doubt this very much, since one of the strongest defenses of the Horcruxes is simply the fact that nobody knows about them. You can see it from Voldemort's anger and terror after hearing about the breaking in of Gringott's, since that meant somebody knew about them and that they could attempt to destroy them. And this means he finally went to check them.
