The result is the name of a buffer. Mostly as it is displayed by the :ls command, but not using special names such as "[No Name]". If {buf} is omitted the current buffer is used. If {buf} is a Number, that buffer number's name is given. Number zero is the alternate buffer for the current window. If {buf} is a String, it is used as a file-pattern to match with the buffer names. This is always done like 'magic' is set and 'cpoptions' is empty. When there is more than one match an empty string is returned. "" or "%" can be used for the current buffer, "#" for the alternate buffer. A full match is preferred, otherwise a match at the start, end or middle of the buffer name is accepted. If you only want a full match then put "^" at the start and "$" at the end of the pattern. Listed buffers are found first. If there is a single match with a listed buffer, that one is returned. Next unlisted buffers are searched for. If the {buf} is a String, but you want to use it as a buffer number, force it to be a Number by adding zero to it:

:echo bufname("3" + 0)

Can also be used as a method:

echo bufnr->bufname()

If the buffer doesn't exist, or doesn't have a name, an empty string is returned.

bufname("#")            alternate buffer name
bufname(3)              name of buffer 3
bufname("%")            name of current buffer
bufname("file2")        name of buffer where "file2" matches.

Obsolete name: buffer_name().