TBH, you give out your "account number, account name and the routing number for (your) bank" every time you write a check and give it to someone.
But... yes, someone asking for that information can be safely assumed to be acting in a nefarious manner. If he's really being honest, give him your PayPal/Zelle/Venmo/etc account name and he can easily send you the money justlike everyone else electronically transfers money.
No, you are not getting robbed (which per law is being forced to do something, i.e. at the point of a gun etc.), stolen from (theft = robbery without forcing you) and also not being hacked (which would indicate someone accessing your online banking or the bank computer systems).
You are likely getting scammed, which is being made to do something utterly stupid by being naive.
Here is how it may go.
The person gets your account information. This is totally valid - I don't want to know how many people have the information to my accounts. Heck, it is on most letters I send out. See, if you want to be paid, people need it. If you run a business, where I am, it MUST be on your letterhead.
The person hacks SOMEONE ELSE and uses his account to send you money. Or the person has someone else pay in cash and send it to you from illegal activity (worse), lets focus on the first case.
The person then may contact you and have you send him the money back, or forward it. This may even look like a job (yea, we don't have a local representative blablabla).
Some time later, the person hacked informs the bank, the sent money is taken from your account (or a debt created) because the transfer is reversed.
You are liable.
But you are not only liable for the money. You may also face charges. You are, depending where the money comes from, complicit in hacking, theft and or money laundering or simply operating an unlicensed money transfer business. Jail time MAY come. Worst case is that it is drug money you help laundering, or financing for some terrorism organization.
This is a well known fact - spend a minute on google and you can find a LOT of examples, e.g. https://www.scamwatch.gov.au/types-of-scams/buying-or-selling/overpayment-scamsor the Wikipedia site at https://en.wikipedia.org/wiki/Money_muleThere are warnings here https://www.westernunion.com/us/en/fraudawareness/fraud-types.html or here http://corporate.moneygram.com/compliance/fraud-prevention/common-consumer-scams
But no, none of them are hacking or robbery.
But they are going to tell you don't give that information out to "some guy".*
This smells like a scam, but you know that.
If this guy wants to send you money, there are several legit ways he can do it. For instance, PayPal, and as a purchase, where you will have seller protection. The scammer will strongly prefer "gift" mode, which he can reverse at will; this is bad for you, don't allow it. However even this does not guarantee that "some guy" isn't using a hacked PayPal account, or using a throwaway PayPal account to use stolen credit cards or bank credentials. And then PayPal could reverse it after all, some time later.
None of this is safe; most payment methods can be reversed by the scammer after you have done the exchange. Well, Western Union and Bitcoin are irreversible, but you'll never find a scammer sending you money that way: they want it the other way 'round! The crux of these scams is send you money in a way they can reverse (take back), and you send money in an irreversible way. Guess what happens next.
Your banker may also be able to assist. And involving a third party is a very good idea. This will mean you are doing the transaction publicly, openly and honestly, which will make it more difficult to accuse you of money laundering.
* Yes, that information is on the bottom of every check**. But there's a big difference: you give checks to people you actually know -- you're mailing it to the gas company or you're handing it to a bricks-and-mortar small business where you know where they live. And that business owner trusts you or they wouldn't take your check. (Maybe on items of negligible cost like fancy coffee, museum admission or movie popcorn; Mac Pro, nope.) I cashiered a big-ticket low-margin retail store for 7 years, a museum for 10 and was also an early eBay seller before PayPal existed. It's been educational.
** For our Euro guests, "check" is an IOU on fancy paper, with a bunch of bank-side infrastructure so you can deposit in your bank (and it debits my account at my bank). (and it's also supposed to be exchangeable for cash at my bank). Awkward, expensive to run, and America is still into it (as well as not putting chip readers on our cards even though the liability shift was in 2015). It reflects a financial infrastructure built on trust, which is fading fast with online transactions and scams.