But the scheme has outraged some in the Ugandan government. Officials such as James Buturo, the ethics and integrity minister, have condemned the Uganda Village Project, which Hornsleth launched in June, as racist.
Hornsleth has mounted the resulting photographs in an exhibition in Copenhagen, depicting villagers showing their "identity cards" in the red, yellow and black of Uganda's flag and each with the name "Hornsleth".
"It's a remark about hypocrisy, about Western and Third World relations, about aid against free trade," Hornsleth told Reuters by telephone from Copenhagen. The project also echoes corporate sponsorship deals.
Ugandan newspapers have filled up with letters and columns, some praising, but many angrily condemning the "pig-for-name" project, as an insult to poor Ugandans.
But for villagers who have taken part, the benefits are clear.
"We're so grateful for these animals," said Kabaalu Muyiwe Hornsleth, trudging through a field of banana plants towards her new goat tied to a tree in Buteyongera village, central Uganda. "Who cares about a name? We're poor and he helped us."
At the side of a dirt road cutting through central Uganda's lush green countryside, a big sign in Ugandan flag colours with the name "Hornsleth" painted on it pokes out of a clearing among rows of banana plants.
To its side lies a neat village full of pig pens, each one fenced in with wooden poles painted red and black, and inscribed with Hornsleth's name.
Local press reported that Uganda's immigration department had rejected passport applications for over 100 Hornsleths wanting to go to Denmark to view the exhibition.
"It is an insult to the sovereignty of Uganda," Buturo said. "In what kind of situation does someone say 'whatever aid I give you, you have to go and change your name?'"
"Africans adopting European names for gifts - we've been doing that since colonial times. Why do you think I am called George?"
Some Ugandans accuse the government of hypocrisy.
"I don't see why government has a problem with helping the poor. They've given us nothing in 20 years of power," said Robinah Namboozo Hornsleth, 38, as she sat on the floor of a windowless clay hut peeling raw cassava into a metal bowl.
"If Hornsleth were offering 100,000 goats for each name change ... the villagers would have been chased from Buteyongera and the Big People would have resettled themselves (there)," Charles Onyango-Obbo, a Daily Monitor columnist, wrote last week.
George Sabadu, a 46 year-old Uganda, said: "Africans adopting European names for gifts - we've been doing that since colonial times. Why do you think I am called George?"
Hornsleth is adamant his project should not be seen as charity, but as an exchange.
"It's not a donation, it's a service. I don't believe in aid, I believe in free trade."
But for the beneficiaries of Hornsleth's idea, the practical help beats any lofty philosophical statement.
"We are not artists, we're just trying to survive," said Luwaga Ahamada Hornsleth, 29. "He gives us goats for free and we just have to advertise his message. That's a good deal."
And villager Henry Kayondo Hornsleth said he would like to apply to the council for permission to change Buteyongera's name to Hornsleth, but said he was unsure whether he would get it.