Jimmy Ward, a father who was in his 30s, was shot dead at the Calcutt Traveller Site near Cricklade, on the outskirts of Swindon, on Sunday morning, Wiltshire Police said.
Emergency services were called to the site just after 8.15am. Despite the efforts of paramedics, Mr Ward was pronounced dead at the scene.
A residential street has been cordoned off following the shooting, and a white forensic tent remains in place at the site.
Wiltshire Police have launched a murder investigation into the incident. A man in his 70s and a woman in her 40s have been arrested on suspicion of possessing a firearm and assisting an offender. Both remain in police custody.
Tributes to Jimmy Ward
Tributes have poured in for Mr Ward, who it is believed leaves behind a wife and children.
One mourner wrote: "RIP to my daughter-in-law's dad Jimmy Ward. Please everyone pray for all the family, my heart goes out to them all."
"Very hard to believe. Rest in heavenly peace my cousin Jimmy Ward," added another.
"Thinking of all the family and friends at this very sad time, sending lots of love to his wife and children. Far too young to die, rest in peace," said another local. Others have described him as "a gentleman."
Calcutt Traveller Site
The Calcutt Traveller Site is a permanent, council-approved Gypsy and Traveller site near Cricklade in Wiltshire.
Police appeal for witnesses
Detective Chief Inspector Phil Walker, from Wiltshire Police's Major Crime Investigation Team, said: "This is an incredibly serious incident, and my thoughts are with the victim's friends and family at this devastating time."
"Enquiries are ongoing at the site and in the wider area to establish the circumstances which have led to this incident and locate all the people involved," he said.
He urged people to respect the cordon and road closure while the investigation continues, and appealed for anyone who witnessed the shooting or saw anything suspicious in the area on Sunday morning to come forward.
Anyone with information is asked to contact police on 101, quoting log 95 of August 2. Information can also be passed to Crimestoppers anonymously on 0800 555 111.
