to start giving personalised gifts so they don't get regifted back to me?

Because you’re purely giving them so that they don’t regift them. And they’re stuck with stuff they don’t want that has their name on.

DH’s aunt and uncle are notorious regifters, which I would have less issue with if they hadn’t one Christmas regifted a food gift we’d bought them the previous year and noticeably peeled off the use by labels. That was actually dangerous so the present went in the bin. And I was sad because I knew that they enjoyed the food we had given them so why not just eat it? I think they must regift everything they are given, and that certainly explains some of the more random gifts we’ve received over the years.

The only way I have found round this is to give them home made fudge and cake, which I know then is appreciated and gets eaten, as the fudge gets opened more or less immediately. And I’m fine with that. But I would also be happy with a mutual decision to stop gifting as we all have too much stuff lying around as it is.

Because you’re personalising it just so it doesn’t get regifted, rather than choosing something they’d like.

Just explain that with the cost of living, you’d rather stop gifts and instead get them a bunch of flowers.

But surely this is exactly what you're doing?

Sorry OP but I'm on the side of the receiver here. I absolutely HATE getting given stuff I don't want and then feeling obligated to keep it to make someone else happy. It IS about you not them if you're giving them stuff they don't want. It's not thoughtful or generous (sorry).
Just don't get them anything. Take them out for coffee / dinner / a drink / an activity instead of you want to "give" them something. Or don't bother. They probably don't want anything anyway.

That sounds ridiculous to me. Stop gifting at all unless you're absolutely certain that person would want whatever it is. Adults buy their own stuff.

I have a friend whose family 'swaps' money every Christmas. It's crazy.

Buying personalised stuff will just mean that it ends up in charity shops where it will stay for a while before landfill. Don't do that. Stop buying 'stuff'.

That’s only really relevant to this thread if you regift it to the person who bought it for you in the first place, as is happening in the OP.

I always re-gift alcohol.
I'm not tee-total, but pretty close to it, and keep getting alcohol as presents. I just re-wrap it, and pass it on to the next person! Most recently was a bottle of Disarono liqueur.

I wish!
There is a particular item I quite like the look of but have never got round to buying for myself. Twice,though, I have bought it for other people who I am pretty sure it would appeal to.
Neither of them have bought it for me or regifted it!

charity shops are full of personalised gifts no one wants.
besides if they know someone with the right name they will have it instead
no if its important why not ask them if instead you get a day out? an afternoon tea? Spa day?

Who are these people to you? Family or friends?

not that it makes much difference, but just say to them New Year, new plan, no more gifts. Less wasteful and no unnecessary spending

This is a really bad idea. Just because you like something or think something is useful, it doesn’t mean everyone else feels the same way. You’re just lumbering him with shit he doesn’t want that will ultimately end up in landfill. either don’t get him anything or ask for a specific gift to get him.
As someone who is often the recipient of shit other people think I’d like, it’s incredibly annoying to have to act so grateful when all I thinking is why do you keep giving me this stuff and how can I offload it without being offensive.

There's a group on FB called "crap you find in charity shops". So much of the stuff posted on there is personalized tat which wouldn't appeal to many people! Who wants a set of champagne flutes with "Mr & Mrs Smith, 5 March 2013" engraved on them?? Not even Mr & Mrs Smith want them.

Unwanted personalised gifts are far, far more wasteful than unwanted generic gifts. For this reason I'd say YABU. It's making it about the giver, not the receiver.

Maybe just agree not to do gifts?

Yabu. Personalised gifts are more likely to be thrown in the bin if unwanted.

Give fewer gifts.
People obviously don't want or need them.
We all have too much stuff.

Personalised gifts are a waste of money (and resources!). Useless to pretty much anyone else.

Just put forward the idea of not buying gifts any more.

I'd be telling people that "it's difficult to get gifts people like and I've been gifted back various things I got various people so I'm no longer buying gifts. Please don't buy he anything for Christmas or birthdays as I won't he reciprocating. I'm telling all my friends and relatives the same thing. Instead lets go out for coffee/lunch/dinner. How does that sound?

I would call them out on this and just say 'as you re-gifted the gift I got you back to me how about we don't no longer exchange gifts?' Just be pleasant about it. There's no point you wasting time and money if they can't be bothered to put the effort in

Is it happening a lot?

Give something you'd like back? 

The problem is, then the people will just have something they don’t want, but with their name on 🤷🏻‍♀️.
Time to knock the pointless gift giving on the head.