Buzz Aldrin carried out a private and quiet communion service on the Moon after landing and just before they exited the lunar module. It happened when he said:

“"Houston, this is Eagle. This is the LM Pilot speaking. I would, like to request a few moments of silence. I would like to invite each person listening in, wherever and whomever he may be, to contemplate for a moment the events of the past few hours and to give thanks in his own individual way."

His account of it in detail is here: Guideposts Classics: Buzz Aldrin on Communion in Space. He didn’t talk about it until much later.

This is not exactly secret, but kind of fun and not many people know it. The first “flag” like object unfurled on the Moon was not the American flag. It was a blank sheet produced by the Swiss to capture the solar wind, and was the first experiment they deployed, before the US flag. It consisted of an aluminium foil sheet, 1.4 m by 0.3 m, fixed to a pole facing the Sun. They deployed it first to maximize its exposure to the solar wind.

Buzz Aldrin standing next to the blank “Swiss flag” experiment. It was also the only non US experiment on the flight. First 'flag' on the Moon?

This “flag” was detached from its pole at the end of their time on the Moon and returned to Earth for analysis. Solar Wind Composition Experiment

When Neil Armstrong died, his widow found a secret stash of pieces of hardware from the Apollo 11 mission in a white bag. Secret stash of Moon artifacts found hidden in Neil Armstrong's closet

The astronauts scribbled notes on the inside of the Command module during the mission - something only discovered this year (2016) through 3D scans.

And:

(Says “SMELLY WASTE” above the PPK sign)

Those were written during the flight. Michael Collins also crawled back in after splashdown to write this (this has been known for a long time, not one of the newly discovered graffiti):

“Following splashdown,while en route to Hawaii on the USS Hornet, Michael Collins crawled back into the command module (it was connected to the mobile quarantine facility by an air-tight tunnel) and wrote this short note on one of the equipment bay panels. The inscription reads:

Spacecraft 107, alias Apollo 11, alias ‘Columbia.’
The Best Ship to Come Down the Line. God Bless Her.
Michael Collins, CMP”
Michael Collins' Inscription inside Apollo 11 Command Module "Columbia"

This shows how they did it. Basically taking lots of photos from inside the module, along with doing laser scans of it all.

The Smithsonian is 3-D scanning Apollo 11 to share with the digital generation

More images and details here:

Apollo 11: The Writings on the Wall - AirSpace

The reason they weren’t found before is because nobody can enter the craft. Even while doing this scan they weren’t permitted to go inside but did it from outside. The aim is to create a virtual 3D version of the module for anyone to download and explore or make a 3D print of it. It was a very challenging project apparently

"We tried to determine how to provide the most possible access to the data collecting technology, but at the same time, protect the object and not damage it," said Needell. "We decided that [the people collecting the data] could not get in and sit in the seats, for instance, nor could they build a platform to put scanners physically inside the command module."

“Needell and his team also decided that they would provide access to the lower equipment bay, the area located below the astronauts' seats, which housed the ship's navigation sextant, telescope and computer.”

"No one from the Smithsonian, as far I knew — not as long as I've been the curator for 20 years, has ever been below there to document the conditions or any of the aspects of the lower equipment bay," said Needell. "We've been able to sort of see above the seats, but that's about all."

From: Apollo 11 astronauts wrote on moon ship's walls, Smithsonian 3D scan reveals | collectSPACE

They removed a big bag of stuff, and beneath that they saw the graffiti for the first time.

See also: Apollo 11 Crew Wrote on Moon Ship Walls, Smithsonian 3D Scan Reveals

Also: Analysis of Handwritten Notes Inside the Cabin of Apollo 11 Spacecraft CM-107 "Columbia"