What word would denote a person who connects a person to another person who has the same needs, situation or struggles? example: Cathy is a good _________. Cathy introduced Jan and Sarah to each other because Jan and Sarah both have similar medical conditions for instance or both live in the same neighborhood for example.
The general term for someone who specializes in matching supply and demand is a broker.
This is how OED puts it:
II. One who acts as a middleman in bargains.
3a. ‘One employed as a middleman to transact business or negotiate bargains between different merchants or individuals’ (McCulloch). Formerly used more widely, including the senses of ‘jobber, agent, factor, commission-agent’.
5a. A middleman, intermediary, or agent generally; an interpreter, messenger, commissioner.
In other words, this is the famous "middleman" in "cut out the middleman".
The etymology of broker derives from Old French broceur "small trader". The earlier etymology is uncertain, but Etymonline speculates it's possibly from Old French brocheor meaning "wine retailer", which comes from the verb brochier, or "to broach (a keg)". In other words, a trader who finds people who make wine and people who drink wine and facilitates transactions between the two.
But of course, brokerage, or intermediation, is older than wine, and is a very varied field. The general impetus behind the rise of middlemen is that suppliers specialize in creating the good or service, and consumers desire the good or service in order to meet some other end, but neither supplier nor consume specialize in searching for counterparties, and often don't have the time or will to put into the search themselves. Thus they trade capital for time and outsource the work.
Given these facts, the role of broker, or middleman, has independently arisen in an enormous variety of contexts, and therefore has been given an enormous variety of names. Some of these might suit your need better than others.
Of course, there are the obvious examples of specific intermediary specialities whose name is simply "-broker" modified by the appropriate attributive noun:
- stockbroker, who buys and sells financial securities to and from issuers and investors,
- the real-estate broker who, employed by the buyer, understands their needs, desires, and budget at a detailed level and surveys the market for matching houses, or employed by the seller, understand the house and its attributes in detail, and seeks buyers who are willing to pay the most for that property,
- the pawnbroker, who matches capital with need (i.e. makes loans), as well as makes markets in the goods forfeited as security for those loans.
- the more metaphorical power broker, who influences distribution of political/economic power by exerting influence or by intrigue (i.e. he's a middle man for power)
etc, but there are also a variety of different kinds of brokers whose titles and role don't include the word "broker" at all:
- the recruiter or (more pejoratively) headhunter who tries to match job openings posted by employers with candidates who have specific education and experience and vice versa
- the matchmaker, who helps arrange dates or marriages, seeking to create a compatible and loving couple based on their personalities and desires. These, in turn, go by different names in different cultures, such as a shadchan¹ in Jewish culture or méirén (媒人)² in Chinese culture. Sometimes matchmakers are indeed called (as bit sarcastically, because it casts love as a business transaction) love brokers.
- Continuing the financial examples from stockbroker, on certain exchanges in the US and abroad, a very specific kind of broker is literally named the specialist, who has a specific list of securities he specializes in, and is responsible for matching supply and demand to create fair and orderly markets. When not specifically designated by an exchange, the more general term for this role is market maker (of "high-frequency trading" fame).
Filling in the blank
Cathy is a good _________. Cathy introduced Jan and Sarah to each other because Jan and Sarah both have similar medical conditions or instance or both live in the same neighborhood for example.
Given the foregoing, and the amazing variety of terms for specific kinds of brokers in the world, the specific label you choose for Cathy will depend on Cathy's reasons for introducing Jan and Sarah.
If Cathy thinks they'd make a good couple, she might be a matchmaker. If Sarah runs a company and Jan would be a good fit for an open position, Cathy would be a recruiter. And so on.
But the key element is Cathy is engaging in brokerage, by whatever name, so the word you're seeking will be some specialized hyponym of broker. If you want to keep it generic and not comment on the reason Cathy is making the introduction, they you can stay with the more general broker or intermediary.
¹ Or sometimes, post the 1964 musical fiddler on the roof, a yenta.
² But this is nuanced and evolving linguistic territory, which I'm not qualified to make statements about, so I'll just quote Prof. David K. Jordan of UC San Diego on the topic:
Footnote #15: Evolving linguistic nuances are such that this may or may not exactly correspond with the generic Chinese term méirén 媒人. For the mainland it seems to correspond closely with jièshàorén 介绍人 (or in the case of the most professional individuals, with hóngniáng 红娘). For Taiwan perhaps it corresponds most colloquially with a verb: a "matchmaker" is a person who happens to zuòméi 做媒 / 做媒. There are, of course, many alternative terms and associated euphemisms. One matchmaker I interviewed consistently referred to each arranged marriage as a "happy match and harmonious union" (jiéwéi liángyuán 结为良缘). Some English writers prefer other terms: marriage broker, go-between. I have not found it useful to try to draw distinctions among such terms.