If I were to admit that, some people might think that it is unfair because he didn't really find the job on his own merit. On the other hand, not admitting it might look like if I were hiding something relatively meaningful and therefore as if I didn't trust them, and the HR managers I talked with to recommend him will see me as a liar.
Maybe I am overthinking this?
Some companies even set out a bounty if you can recommend someone who they actually hire.
People should only "recommend" candidates they know reasonably well. And knowing someone reasonably well often implies friendship.
However: Some people arrange a friend/spouse/relative to get a position at their company, while not being sure that they will do a good job. In that case it might be quite helpful to keep their mouths shut. It would have been even more helpful not to introduce someone who is not a good fit in the fist place.
But as long as you recommend (opposed to "arrange") a friend who has the necessary skills, there is no reason to hide it.
A second thing to look out for: do not let friendship interfere with decisions at work. If you end up working together do not treat them differently than any other colleague (while working, at least).
If you refereed your friend through proper channel and you were not involved in the hiring process, there is absolutely no problem is disclosing that you are friends. That's what referrals are for.
Note the difference between referring (or recommending) your friend, and getting him the job. The latter implies that you influenced the company to make sure they would hire him; which would be perceived badly.
However, if you merely referred/recommended him to the company for a known vacancy, and the company independently interviewed and hired your friend; then you have done nothing wrong.
Some people might think that it to be unfair because he didn't really find the job on his own merit.
It's not about finding the job. The skill is not in managing to find the vacancy. The skill is in getting the company to agree that you are the right employee for the vacancy and offer to hire you. This is not impacted by how you came to know about the vacancy in the first place.
All you did was point out that there's a vacancy. You did not in any way make the interview easier for them than it would've been for others (I assume).
On the other hand, not admitting it might look like if I were hiding something relatively meaningful
Yep, it suggests a guilty conscience. Even if there is none, it will be inferred.
Maybe I am overthinking this?
I think you are.
Simply make sure to not imply that you got him the job. That implies that you did unfairly benefit your friend in the hiring process.
It is not a problem that you disclose your relationships with that person, in fact, it is sometimes desired if you know that person well enough and can provide detailed information about their skills or abilities. Companies will favor reference from their existing, trusted employees, who know the work to be done and can assess the skills of that particular person, rather than looking out in the wild for somebody who nobody knows to cover that vacancy.
The problem would be if you had any executive power towards the hiring process (for example, you are a hiring manager) and you were biased in your decision making process.
But if all you did was a recommendation, and you made your disclosure about it, the decision process will be made by the company, and your recommendation will only be a positive note in the full record of that person in the HR's paperwork.
However, make sure you recommend people who you think (to the best of your knowledge) that are suitable for the job, as if they were complete strangers. Do not recommend in a friend that might not be the most skilled worker just for the sake of working with him, if he is blatantly unprepared, this could affect the amount of trust that your recommendations will get in the future.
If I were to admit that, some people might think that it to be unfair because he didn't really find the job on his own merit.
I am curious why you think he didn't get the job on his own merit? Are you senior enough that your referral alone would carry enough weight to influence the process?
If you're at a very senior level then people below you may feel pressured to hire your friend. However if you're just a normal worker and the person making the hiring decision is senior I really wouldn't worry.
I doubt your referral carries enough weight to influence the decision and it sounds like your friend passed the normal interview process. Unless you fed him answers so he would ace the interview then within a week of him starting no one will care that you handed his CV to HR.
