You should talk with your neighbour to find out what the problem is and how he/she wants it to be solved. Discuss whether that solution works. If it doesn’t, work out a compromise. Hopefully your neighbour is a reasonable person.
If your dog barks a lot, or has other annoying behaviour, you must do something about it. Perhaps build a fence to keep it at home, or get a training collar to stop the barking, or meds from the vet to calm it down and keep quiet.
If your dog is aggressive, you must constrain it for everyone’s safety. Just because it is cute in your opinion does not mean that it really is safe for strangers. Some dogs feel threatened by strangers or by other dogs and must be retrained with a training harness or even muzzle. I never take my dog out without a muzzle-type of harness for this reason and she’s long past the puppy stage. Some dogs just are like this. Perhaps they can be trained if you can afford a trainer.
Those are some reasons people have problems with dogs. The most obvious one: Do you pick up after your dog poops? If not, yeah, your neighbour is going to complain. Do you keep it on a leash when on public property? Do you obey the dog laws of your jurisdiction? Do you get it checked by a vet annually and keep it up-to-date with rabies shots? What about feeding it properly and paying dog tax? Your neighbour will eventually notice if you don’t and get on your case because all of these things are the duty of every responsible dog owner.