Why do primary keys have names of their own

From a mathematical view, granted that a table has at most one primary key, it seems to be a shortsighted design decision to refer to primary keys by some arbitrary name instead of a simple table property.

As consequence to change a primary key from nonclustered to clustered or vice versa, you have first to search for its name, than drop it and finally readd it.

Is there some advantage in using arbitrary names that I do not see or are there DBMS not using arbitrary names for primary keys?

Edit 2011-02-22 (02/22/2011 for those who don't want to sort there date):

Let my show the function, with which you can derive the names of a primary key from its tables name (using early sql-sever aka sybase system tables):

create function dbo.get_pk (@tablename sysname)
returns sysname
as
begin
    return (select k.name
    from sysobjects o 
        join sysobjects k   on k.parent_obj = o.id 
    where o.name = @tablename
    and o.type = 'U'
    and k.type = 'k')
end
go

As gbn states no people really like the generated name, when you do not supply an explicit name:

create table example_table (
    id int primary key
)

select dbo.get_pk('example_table')  

I just got

PK__example___3213E83F527E2E1D

But why must names in sysobjects be unique. It would be perfectly OK to use exactly the same name for the table and its primary key.

Doing it that way, we didn't need to set up naming conventions, which could be accidentally violated.

Now answers to Marian:

1. I only used the task of changing a
   clustered into a nonclustered
   primary key as an example where I
   need to know the actual name of the
   pk to be able to drop it.
2. Things don't need to have proper
   names, it is sufficient if they can
   easily uniquely denoted. That is the
   basis of abstraction. Object
   orientated programming goes this
   way. You need not use different
   names for similar properties of
   different classes.
3. It is arbitrary, because it is a
   property of a table. The name of the
   table is all you need to know if you
   want to use it.