Not as far as we know.
No house-elf is ever referred to by more than a single name in any canonical materials - books, Pottermore, or even films. Dobby, Winky, and Kreacher are always called simply Dobby, Winky, and Kreacher, not Dobby Malfoy, Winky Crouch, Kreacher Black, or by surnames of their own.
According to Wikipedia (which is of course not a canon source, but it's the best I could find):
House-elves are small elves used by wizards as slaves. They are 2–3 feet tall, with spindly limbs and oversized heads and eyes. They have pointed, bat-like ears and high, squeaky voices. Their names are usually pet-like diminutives, and they do not appear to have surnames. They habitually refer to themselves in the third person.
But we don't really know much about house-elf culture, if indeed they have any culture among themselves beyond simply serving wizardkind. So it is possible that house-elves have surnames which they might use to each other, but the wizards they serve simply don't care and refer to them by a single name because it's easier. (I've previously discussed the issue of house-elf culture here.)