Problem with real estate agency

I got contacted today by a third person, talking to a real estate agency on my behalf, that my neighbor contacted a real estate agency about man's voice coming from my apartment. He said that I am living with the man he heard.
I have had a boyfriend for almost half a year now, who has his own apartment, but because mine is bigger and much better furnished, we spend most of our free time at my place and most of the week he also sleeps over.
I told a third person he does not live with me, that I have a boyfriend who comes over and spends time at my place, but he has his own place, where his residence card is also registered. She said she will talk to the agency.

However, I would like to know what to expect next. Do real estate agencies check on their tenants in such cases? Should I pay additional 3,000 yen for him, just to be at peace?

「we spend most of our free time at my place and most of the week he also sleeps over. I told a third person he does not live with me, that I have a boyfriend who comes over and spends time at my place, but he has his own place, where his residence card is also registered. 」
If a person routinely spends "most of his free time" in an apartment and also sleeps there most nights, in practical terms, he lives there. If your lease is for a single occupant, the situation with you and your boyfriend may be in violation of that.

「However, I would like to know what to expect next. Do real estate agencies check on their tenants in such cases? Should I pay additional 3,000 yen for him, just to be at peace?」
From what I can gather, Person A told Person B that they were going to talk to your landlord, so yes your landlord may contact you to find out what's going on.

I'm not sure what the 3,000 yen is referring to. Does your lease have a clause that a second occupant is allowed in your apartment for a 3,000-yen increase in the monthly rent? If your boyfriend is sleeping most nights in your apartment, then yes, they may ask you to pay that additional fee.

「my neighbor contacted a real estate agency about man's voice coming from my apartment. 」
On a side note, if your neighbor's can hear your boyfriend's voice through their walls, you might want to ask him to be quieter. It might be that your neighbor doesn't really care whether or not you have someone living with you, but that the noise your boyfriend is making is what's really bothering him.

Years ago when I started living on my own, and was looking at renting a small studio apartment (where only single occupancy was allowed), I checked with the estate agency if it is okay someone stays over; at that time it was my boyfriend who might stay just for the weekend, but I thought it would be better to be honest about it. (The landlord was living far away.) They told me that it is a matter of how often, and if not often that should be OK. So we left it at that. He came maybe two times a month, staying for the weekend.

In your case, since you mention some amount, the landlord allows two occupants I assume, so if he is at your place more than half the time, I would register him as an occupant/frequent visitor and pay that (if I were you). This is just to let them know in a way who are frequenting the premises.

I don’t think the estate agent is going to come check on you just to see whether you have some un-registered resident there, UNLESS they are very close to the owner and would avoid any trouble for the owner at any cost.

But I agree with the other poster; the voice might be what is bothering the next door neighbor more than “someone else living there.” So if the neighbor complains again, they might call you to warm you, or start putting up posters in the entrance requesting everyone to be mindful of noise at night, or something like that.