With the libmcrypt-2.4.x and libmcrypt-2.5.x API these constants also work, but it is possible to specify the name of the cipher as a string with a call to mcrypt_module_open().
Here is a short list of ciphers which are currently supported by the mcrypt extension. If a cipher is not listed here, but is listed by mcrypt as supported, you can safely assume that this documentation is outdated.