It depends on the license!
Some licenses' texts specify what can be done with them; e.g. the GPL v3 starts with
Copyright (C) 2007 Free Software Foundation, Inc. http://fsf.org/
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
So you're allowed to copy the whole document, which includes its title. And the application instructions of the GPL specify that the license should be named in the files it covers (see Should I include license text in a single file or all source files? for further discussion of this).
The MIT license doesn't carry any such provision. (It does specify that the license must be reproduced in derivative works, as-is, but that's valid once it's been chosen for a work.) In fact "MIT license" is a name given after the fact to licenses used at MIT, which had slight variations themselves. (The version in common use is the Expat license.) The OSI added a title to the license in their page describing it, but that isn't part of the text used even by the original authors of the license...
So while it is nice to name the license used by a project, it isn't always necessary, and you'll find lots of projects which don't name their license (especially when it's a BSD-style license, the Expat license, the zlib license, or the ISC license) — people aren't necessarily all that concerned with cataloguing license usage, just with granting rights.