The Spanish tennis ace is seen as the player to take up the country's mantle in the sport following the retirement of his childhood hero but admits that the similarities between the pair can be unhelpful at times.
Speaking in the new Netflix documentary 'Carlos Alcaraz: My Way', he said: "I don't want to be called Rafa's successor.
"I want to be called Carlos Alcaraz Garfia."
Nadal can understand Alcaraz's frustration on the matter and warned against putting too much pressure on the young player's shoulders.
The 22-time major winner said: "When you're young and they're constantly comparing you to some professional that's been on the circuit for many years, there are times you get tired of hearing it.
"This leads to an excess of pressure and in the end, I think it can distort your daily life and even confuse you."
The Netflix documentary follows Alcaraz during the 2024 season - where he won both the French Open and Wimbledon - and the world number three confesses that he struggles to balance his personal life and professional career.
He said: "I guess right now my fear would be that tennis becomes an obligation."
Alcaraz speaks about going on holiday to Ibiza following his loss to Novak Djokovic in the 2023 French Open semi-final and thinks that the time away from the court helped him bounce back strongly to win Wimbledon shortly afterwards.
The four-time Grand Slam champion said: "I wanted to go there basically to just get wasted.
"I made the most of it because I knew I might not get another three days like that. When I got back, of course, I won Queen's and Wimbledon.
"I'm not saying partying helped me win, but taking that time off was good for me."