CHICAGO — The Giants finally have a rough date for Johnny Cueto’s return from Tommy John surgery.

Manager Bruce Bochy said Cueto could pitch for the Giants around Sept. 8 after two rehab starts for Triple-A Sacramento. The first likely will be Monday against Reno at Raley Field.

In a start for Class A San Jose at Modesto on Tuesday night, Cueto allowed five runs (four earned) on four hits in 4 ⅓ innings. He struck out three and walked one.

In his first three rehab games, Cueto threw 6 ⅔ innings and allowed one earned run, with nine strikeouts. He had no walks. It’s hard to walk kids in rookie ball and Class A when they are facing a big-league pitcher. They want to connect.

Two games for Sacramento would give Cueto six rehab starts, which was the plan. A Sept. 8 return would be at Dodger Stadium in the final game of the Giants’ penultimate trip, and a shade more than 13 months after his surgery.

Feting Samardzija: The Giants held a private celebration for pitcher Jeff Samardzija on Sunday for reaching 10 years of major-league service time, a milestone that guarantees a full big-league pension and stands as a symbol of endurance.

“I got a shark cake, a lot of butt slaps and a lot of attaboys, but when half your team already has 10 years, it’s not really that special,” he joked.

The 34-year-old faces his original club at Wrigley Field on Thursday.

As for reaching 10 years, Samardzija said, “It’s very humbling and I’m very proud of it. It hasn’t been easy and I’m proud of how many adjustments you have to make to be here with getting older. I’m a very stubborn guy, so I’m very proud I was able to make adjustments along the way.”

Duggar update: Center fielder Stephen Duggar figured he was headed for surgery after he made a diving catch at Oracle Park on Aug. 7 and sprained the same left shoulder he dislocated the year before. Duggar was told the sprain was serious, a Grade 3.

Dr. Neal ElAttrache had a different view after examining Duggar in Los Angeles on Tuesday and recommended rehab that would last four to six weeks.

“That’s the best news we could have gotten. He’s not looking at surgery,” Bochy said.

Duggar is on the 60-day injured list, so his regular season is over.

Dr. ElAttrache, one of the nation's premier orthopedic surgeons, will see another Giants player Wednesday, as Pablo Sandoval was to fly to Los Angeles to have his right elbow examined.

Sandoval was placed on the injured list with inflammation caused by bone spurs, which he has had for some time. Surgery remains possible.

Rotation: The Giants will have a second day off in five days Friday. Although Logan Webb would pitch against the A’s on Saturday and Madison Bumgarner on Sunday if the starters stayed on turn, Bochy could flop them so Bumgarner need not go a week between starts.

Henry Schulman is a San Francisco Chronicle staff writer.