Your people will see if you are honest and trustworthy, and they will take their cues from you.
If you lie, or fudge the data, or say to your team members: “If the client calls, tell them I’m not here,” then your people will think that it’s acceptable for them to do that, too.
Make sure that your behavior is above reproach. Walk the walk.
And don’t tolerate dishonesty on your team. Set your expectations. State your expectations. Make sure there are consequences for dishonest behavior. You might give someone “who didn’t know any better” a second chance, but don’t give anyone a third chance.
(research source: https://www.linkedin.com/pulse/art-dealing-difficult-people-5-tried-and-true-j-andy-newsom/) (image generated using Midjourney)