For the Apollo mission, there was a debate on which mode is better - the Earth orbit rendezvous (EOR) or the lunar orbit rendezvous (LOR). Who was the first person to introduce the concept of space rendezvous?
The description of the question mentions the Apollo missions, but the title of the question and later comments indicate that the expected answer is something like: 'these' people came up with the concept of orbital rendezvous and suggested how it could be done.
It is obviously impossible to completely prove or verify which human did this first, but the simplified equations that are used for relative motion in orbit are called Euler-Hill equations or Hill-Clohessy–Wiltshire equations. source
Digging a bit further into these names, this is what I found-
Tycho Brahe discovers the inequality with
the mean motion counted from New Moon or Full Moon, he found the Moon about 2/3 of a degree behind its mean position a week before New Moon and before Full Moon, and about 2/3 of a degree ahead of its mean position a week after New Moon and after Full Moon. source
Johann Albrecht Euler(son of Leonhard Euler) formulates this problem in a way different than his predecessors who pondered the 3 body problem. source
George William Hill
provided the first complete mathematical solution to the problem of the apsidal precession of the Moon's orbit around the Earth, a difficult problem in lunar theory first raised in Isaac Newton's Principia Mathematica of 1687. This same work also introduced what is now known in physics and mathematics as the "Hill differential equation", which describes the behavior of a parametric oscillator and which made an important contribution to the mathematical Floquet theory. source
This formulation helps see how 2 bodies orbiting 1 central body behave. And this paper says that the Clohessy-Wiltshire equations were the first to use them as relative motion for spacecraft rendezvous.
W.H.Clohessy and R.S.Wiltshire of The Martin Company published a paper in 1960, titled 'Terminal Guidance System for Satellite Rendezvous.' The paper explains the term Rendezvous, derives equations, describes requirements and so on. This was the earliest one that I could find.
To summarize from above points:
The genesis of the requirement of deliberate Rendezvous was sometime before 1959. W.H.Clohessy and R.S.Wiltshire where probably the first people to show how it could be done. The tools they used however, came from a problem that was discovered in 1590s, formulated in 1776 and well worked on from 1878.
Lunar orbit rendezvous was first proposed in 1919 by Ukrainian engineer Yuri Kondratyuk, as the most economical way of sending a human on a round-trip journey to the Moon.
Dr. John Houbolt would not let the advantages of LOR be ignored. As a member of Lunar Mission Steering Group, Houbolt had been studying various technical aspects of space rendezvous since 1959 and was convinced, like several others at Langley Research Center, that LOR was not only the most feasible way to make it to the Moon before the decade was out, it was the only way. He had reported his findings to NASA on various occasions but felt strongly that the internal task forces (to which he made presentations) were following arbitrarily established "ground rules." According to Houbolt, these ground rules were constraining NASA's thinking about the lunar mission—and causing LOR to be ruled out before it was fairly considered.
In November 1961, Houbolt took the bold step of skipping proper channels and writing a nine-page private letter directly to associate administrator Robert C. Seamans. "Somewhat as a voice in the wilderness," Houbolt protested LOR's exclusion. "Do we want to go to the Moon or not?" the Langley engineer asked. "Why is Nova, with its ponderous size simply just accepted, and why is a much less grandiose scheme involving rendezvous ostracized or put on the defensive? I fully realize that contacting you in this manner is somewhat unorthodox," Houbolt admitted, "but the issues at stake are crucial enough to us all that an unusual course is warranted."
When the Apollo Moon landing program was started in 1961, it was assumed that the three-man command and service module combination (CSM) would be used for takeoff from the lunar surface, and return to Earth. It would therefore have to be landed on the Moon by a larger rocket stage with landing gear legs, resulting in a very large spacecraft (in excess of 100,000 pounds (45,000 kg)) to be sent to the Moon.
If this were done by direct ascent (on a single launch vehicle), the rocket required would have to be extremely large, in the Nova class. The alternative to this would have been Earth orbit rendezvous, in which two or more rockets in the Saturn class would launch parts of the complete spacecraft, which would rendezvous in Earth orbit before departing for the Moon. This would possibly include a separately launched Earth departure stage, or require on-orbit refueling of the empty departure stage.
Wernher von Braun and Heinz-Hermann Koelle of the Army Ballistic Missile Agency presented lunar orbit rendezvous, as an option for reaching the moon efficiently, to the heads of NASA, including Abe Silverstein, in December 1958. During 1959 Conrad Lau of the Chance-Vought Astronautics Division supervised a complete mission plan using lunar orbit rendezvous which was then sent to Silverstein at NASA in January 1960. Tom Dolan, who worked for Lau, was sent to explain the company's proposal to NASA engineers and management in February 1960.  This alternative was then studied and promoted by Jim Chamberlin and Owen Maynard at the Space Task Group in the 1960 early Apollo feasibility studies. This mode allowed a single Saturn V to launch the CSM to the Moon with a smaller LEM.[Note 3] When the combined spacecraft reaches lunar orbit, one of the three astronauts remains with the CSM, while the other two enter the LEM, undock and descend to the surface of the Moon. They then use the ascent stage of the LEM to rejoin the CSM in lunar orbit, then discard the LEM and use the CSM for the return to Earth. This method was brought to the attention of NASA Associate Administrator Robert Seamans by Langley Research Center engineer John C. Houbolt, who led a team to develop it.
Besides requiring less payload, the ability to use a lunar lander designed just for that purpose was another advantage of the LOR approach. The LEM's design gave the astronauts a clear view of their landing site through observation windows approximately 4.6 metres (15 ft) above the surface, as opposed to being on their backs in a Command Module lander, at least 40 or 50 feet (12 or 15 m) above the surface, able to see it only through a television screen.
So the concept of a rendezvous in space was proposed by Yuri Kondratyuk in 1919 and by Hermann Oberth in 1929 and by the member of the British Interplanetary Society Harry E. Ross in 1948.
Wernher von Braun preferred the Earth Orbit Rendezvous at first but was convinced by John Houbolt of the advantages of the Lunar Orbit Rendezvous in a campaign that lasted from 1960 to 1962.