Tayshaun Prince is a Celtic now -- and a Clipper later?

The name across the front of his jersey read “Boston” on Monday, so Tayshaun Prince wouldn’t allow himself to think about what it might be like to have “Clippers” or another team stitched there in a few weeks.

“I’m not going to have one foot in, one foot out,” Prince said before the Celtics’ 102-93 loss to the Clippers at Staples Center. “I’m a Boston Celtic and I’m going to have both feet in.”

Boston acquired Prince last week as part of the trade that sent Jeff Green to the Memphis Grizzlies, but it remains unclear if the veteran small forward will have his contract bought out.

The Clippers are currently without a true backup small forward and would be among the teams interested in adding Prince, 34, if he becomes available.

Celtics Coach Brad Stevens said he was “hopeful” Prince would remain with his team through the end of the season because of Prince’s personality and experience. The 13-year veteran won an NBA title with the Detroit Pistons in 2004 and is considered a positive influence in the locker room.

Prince finished with two points, two rebounds and one assist in 19 minutes off the bench in his Celtics debut Monday, typical production for a player primarily known for his defense.

Would Prince, a Compton native, be interested in joining the Clippers?

“I can’t really speculate on what teams I can help and things like that when I’m sitting here as a Boston Celtic not knowing what the future holds,” he said. “If that situation happens to where down the road where I am free, we’ll get to that situation then.”

Clippers spirit

It was no surprise the first player off the bench to greet Blake Griffin during a timeout in the first quarter Monday after Griffin made a steal and threw an alley-oop pass to DeAndre Jordan for a dunk was Dahntay Jones.

The veteran swingman has become the Clippers’ unofficial head cheerleader during a 10-day contract that ends Saturday.

Jones has led a surge in activity among bench players over the last four games, standing and applauding every highlight made by their teammates.

“It’s my family, my team, I want to win,” Jones said, “so if cheering for them helps the cause that’s what I’m supposed to do.”

Clippers Coach Doc Rivers said the bench was standing so often against Sacramento on Saturday that referees asked players to sit down.

“That’s a good problem to have,” Jones said, “because the alternative is you could look to your bench and see a bunch of guys not interested in the game and then you have no source of energy.”

Signed primarily for his defense, Jones scored his first points with the Clippers on a layup early in the fourth quarter Monday. The team could sign him to another 10-day contract to provide a longer audition.

Jones’ enthusiasm makes him a popular presence but won’t guarantee he sticks around.

“At the end of the day, you want good basketball,” Rivers said. “I mean, that’s going to be the difference.”

ben.bolch@latimes.com

Twitter: @latbbolch