Depending on what you do, there may be a user trust issue. Users may trust you less if your domain is privately registered.
This may not matter for you, depending on what you do. And your users may be unlikely to look this up. (I think the more your site involves technology, the more likely users are to look it up.)
I think my current registrar convinced me that their approach is right. they go halfway. You use them for tech and admin contacts. For .com and .net (not sure about others), this hides your phone number, as there is no phone number needed for registrant identification. (I know that at least some ccTLDs include a phone number in the registrant data, though. For example, Austria, .at. But you can always use voice mail.)
You can use a P.O. Box or private postal service for address. I think at one time you were not allowed to do this, but it currently is allowed.
That leaves just your name. Again, we go to user trust. Would you trust somebody who won't tell you their name?
I'm not sure of the legality of using something like "Domain Administrator" for the name. If you can do that, that leaves just company name, and a PO Box for address.
Or, of course, you could just make it all up.
When I see this, (it's usually obvious) I don't trust them one bit.
You really shouldn't be getting a lot of mail and phone calls. First of all, make sure your number is on the "do not call" list. Also, see if your registrar sells addresses, and if you can opt-out of having your address sold. I haven't gotten a think since I did the latter.
Registrars have various levels of protecting their data from being harvested. Many now use a captcha, so it's impractical to harvest large numbers of addresses.