Welcome to the wonderful, confusing world of objects, semantic models and unintuitive terminology.

The "immutable object" is an abstract kernel of your being, to which all other properties are related. It represents, in a way, the coincidence of all those other properties, but it's not quite so simple.

In semantic modelling, those properties are considered objects too, albeit often dependent ones: "Hair color" in the sense of a person's hair color is an object type; individual instances cannot exist without a person whose hair they're describing. "Blonde", in that sense, is a grouping of instances, but if there were no blonde people, the group would be empty.

Likewise, "Name" is an object type that depends on the thing it's naming. Sure, you can come up with arbitrary terms that don't refer to anything, but they're semantically meaningless. Conversely, a thing can exist without being named, like a newborn. You could identify it as "the newborn baby of ", but that isn't a name so much as list of properties (newborn, parents\¹), that coincide for one particular person.

The combination of a simple object (that a stract kernel) and its dependent objects (properties) forms a complex object. You, as a person, probably have a name by now. You also probably have a body, a past², some knowledge and skills like the ability to understand and form words and sentences, which in turn includes a vocabulary...

If you change your name, that is one property that changes; one dependent object that is swapped out for another. The rest of your properties is unaffected by that. Formally, the relation between you and your name is mutable, but your eye color for instance (probably) isn't dependent on your name.

Now, if you were to somehow swap out all dependent objects at once, changing every property - a different name, different past, different parents, different body - then you would arguably be a different person. Even if you could argue that the core object remains the same, but given that this core object is an abstraction to describe the complex of properties and relations, which no longer has any intersection with the original, that "sameness" is effectively meaningless. The original configuration of properties is no longer tied to anything.

The philosophical difficulty of this concept is the question just what level of change constitutes a different object; which properties are immutably tied to you, so that changing one of them would be a different person? It's the Ship Of Theseus question: How much about a thing can change before it's no longer the same?

Do we argue that, as soon as even one property is changed, it no longer is the same object? Then every moment in time, adding to the past of an object, will make it a new object, nothing is permanent and the immutability is worthless.

For a person, most immutable properties of yours would be part of your past - where you were born, when you were born, essentially the continuous sequence of moments in your existence leading up to this one. The name you were assigned after birth would be a part of that history, even if the name you now use is a different one. Yet we do say that someone has become a different person if things like worldview and patterns of behaviour differ strongly enough. Again we encounter the question: What else, besides your past, defines you?

Practically, most contexts use some subset of your properties to define a person. In the example of a user id, that is the one immutable identification for user management purposes. Change the name, age, login, permissions and everything - from the system's perspective it's still the same user. Semantically, this might be a different person, but the system doesn't care.

Practice has to make concessions to the limitations of human abilities. We accept a level of ambiguity by ignoring some properties, because ultimately every model and pattern is supposed to simplify our decision-making. Overcomplicating things doesn't help us navigate life.

1 Parenthood itself could be modeled a simple, abstract object, dependent on both the parent and the progeny, representing the circumstance that one is the parent of the other. Technically, the Child could then exist independently from having parents; Practically, biology gets in the way of that.

2 Modeling the past of a given object is actually a complex exercise that also runs up against many of the same problems: You could consider it a continuous set of moments, each of which represents a relationship between a point in time and your exact state (coincidence of properties) at that point. But under the assumption of linear time, each moment would describe a different state, at the very least a different set of past moments.