Buffer Names - GNU Emacs Lisp Reference Manual

Each buffer has a unique name, which is a string. Many of the functions that work on buffers accept either a buffer or a buffer name as an argument. Any argument called buffer-or-name is of this sort, and an error is signaled if it is neither a string nor a buffer. Any argument called buffer must be an actual buffer object, not a name.

Buffers that are ephemeral and generally uninteresting to the user have names starting with a space, so that the list-buffers and buffer-menu commands don't mention them. A name starting with space also initially disables recording undo information; see Undo.

— Function: buffer-name &optional buffer

This function returns the name of buffer as a string. If buffer is not supplied, it defaults to the current buffer.
If buffer-name returns nil, it means that buffer has been killed. See Killing Buffers.
          (buffer-name)
               => "buffers.texi"
          
          (setq foo (get-buffer "temp"))
               => #<buffer temp>
          (kill-buffer foo)
               => nil
          (buffer-name foo)
               => nil
          foo
               => #<killed buffer>
     

— Command: rename-buffer newname &optional unique

This function renames the current buffer to newname. An error is signaled if newname is not a string, or if there is already a buffer with that name. The function returns newname.
Ordinarily, rename-buffer signals an error if newname is already in use. However, if unique is non-nil, it modifies newname to make a name that is not in use. Interactively, you can make unique non-nil with a numeric prefix argument. (This is how the command rename-uniquely is implemented.)

— Function: get-buffer buffer-or-name

This function returns the buffer specified by buffer-or-name. If buffer-or-name is a string and there is no buffer with that name, the value is nil. If buffer-or-name is a buffer, it is returned as given; that is not very useful, so the argument is usually a name. For example:
          (setq b (get-buffer "lewis"))
               => #<buffer lewis>
          (get-buffer b)
               => #<buffer lewis>
          (get-buffer "Frazzle-nots")
               => nil
     
See also the function get-buffer-create in Creating Buffers.

— Function: generate-new-buffer-name starting-name &rest ignore

This function returns a name that would be unique for a new buffer—but does not create the buffer. It starts with starting-name, and produces a name not currently in use for any buffer by appending a number inside of ‘<...>’.
If the optional second argument ignore is non-nil, it should be a string; it makes a difference if it is a name in the sequence of names to be tried. That name will be considered acceptable, if it is tried, even if a buffer with that name exists. Thus, if buffers named ‘foo’, ‘foo<2>’, ‘foo<3>’ and ‘foo<4>’ exist,
          (generate-new-buffer-name "foo")
               => "foo<5>"
          (generate-new-buffer-name "foo" "foo<3>")
               => "foo<3>"
          (generate-new-buffer-name "foo" "foo<6>")
               => "foo<5>"
     
See the related function generate-new-buffer in Creating Buffers.

27.3 Buffer Names