I don't know for sure what the current procedure is for name change on Chase credit cards, so I'm not saying your banker was wrong, but branch bankers have a reputation like Disney bus drivers... take some salt with you
My experience was several years ago, like 8 ish I think? So I'm sure it has changed a bit, but I find it hard to believe they would change your card number for a name change. They will reissue the cards in the new name so the security and expiration date may change, but changing the whole number seems extreme. Also not sure that they'll automatically issue expiring cards with the new name at renewal - if it were the case that him changing your bank accounts actually did change the name on your credit card accounts, simply requesting replacement cards for "damage" would issue them in the new name. Actually, I wonder if that's what he was thinking of when he said you'd get new card number, getting replacement cards? But you should only get a new number for lost/stolen cards.
I would call one of your personal cards and see what the procedure is. You may need to fill out a name change form and send it back via secure message. They may be able to do it over the phone given that you changed your bank accounts and they confirmed the documentation already.
And they usually change it on your profile, so all cards on that profile would get changed and you probably don't have to do it for each card individually. But who knows? Maybe someone with more recent experience can chime in. When I did it, the phone rep did it all while I was on the phone, no documentation needed. They asked if the name change was from a marriage , so it might have had less red tape than a legal decree at that time? I was pleasantly shocked at how easy it was to change all my credit cards, I did all but BoA over the phone. I expected more hassle so I had put it off, but after the first issuer did it over the phone I called the rest up and got everything updated in a day or two. (Except BoA, that card is still in my previous name. I applied for a new credit card in my new name, which they were ok with and automatically added it to my existing account with the old card, but won't update the old card without some in person rigamarole. Even opened a checking account in the new name and all 3 are linked together in my online account automatically, which is under the new name, but no go on name change for that card. Whatever. Out of spite (or something?) I just added an AU on that card in the new name on the off chance I use it somewhere that cares.)
So I don't expect it to be as lax as it was when I did it; I also don't think it's as painful as the banker stated.