The Red Bull Junior, who is driving for Trident this year, said he is “very thankful for the last name I have and for the benefits” but said “in one way it only gets you so far”.
Doohan, 18, also said “it would be a lot more were I to take the two-wheeled route”.
His father won five consecutive 500cc World Championships between 1994 and 1998, with only Giacomo Agostini, Valentino Rossi and Marc Marquez having won more.
Doohan Jr had a tough start in F3, finishing 26th for HWA Racelab last year and failing to score a single point.
But he currently sits fifth in the drivers’ championship, with 21 points and one podium from the first round in Barcelona.
Jack Doohan, Trident
Photo by: Formula Motorsport Ltd
Asked if he felt any surname pressure, Doohan said: “I’m obviously very thankful for the last name I have and for the benefits, but you know, in one way it only gets you so far.
“Especially in this game, you don’t perform then you’re out. I feel like after last year I’m very lucky to get another opportunity this year, and a chance to show my potential.
“But on the pressure side of things, I feel, as you said, it would be a lot more were I to take the two-wheeled route, so on the four-wheeled route obviously there’s the slightest bit of pressure, probably.
“It stands out maybe a little bit more on a level probably if you’re not performing.
“But I’m putting that kind of not performing stage in the past and focus on myself, making sure that I’m the best I can be with the team around me and the car I’ve got and hopefully then enjoying the pressure, in a way, if that makes sense.”
F3 returns in support of the French Grand Prix at Circuit Paul Ricard this weekend.