Is there a better term than Hinayana?

In the other answers there are some proposals which I do not want to repeat here; this answer is just to shed some other/private light on some more whereabouts of the problem.

In pre-socialistic Russia there were the two sections of the communist party, one called "menshewiki" the others "bolshewiki". Today most people knows only "bolshewiki" and associate something -possibly special cruel- with it...
Now, well, it only meant:"menshewiki"- the smaller fraction, "bolshewiki" - the larger fraction. "minority"- "majority"....
Of what I've read, the word "mahasanghika" had initially simply some similar connotation, but with the occurence of the term "maha-yana" (the wider/larger vehicle) it must have happened relatively soon that also a connotation far beyond of the size-aspect towards "better/worse", "superior/inferior" overlaid (and possibly dominated) that size-aspect. (A specially intense impression can one get when reading the (mahayana-) Parinirvana-sutra, where even the term itself is mentioned and celebrated as liberation-relevant).
Perhaps, if it had happened using the english language one had called the own, larger, part of the sangha the "omnibus-car", or even "ferrari-car", the "thunderbolt-car", and the smaller, more traditional part the "bobby-car". And the pali-term "hina" means in almost all cases something with a less-worth connotation as some Pali-dictionary had pointed out.

So you can try to imagine that when you say "hinayana" the listener understands "bobbycar" and feels somehow intimidated. The use of the term "theravada" is, again as I understood that things, only a way out of the mess, because originally it meant only a subgroup in that smaller fraction of descendents of the initial sangha. But it seems, it is the only surviving one of them and one might accept, that their name is taken "pars-pro-toto".

I'm just reading An Introduction to Buddhism by Peter Harvey. He uses a geographically based model which I like so

• Southern Buddhism - Theravada (Burma, Laos, Cambodia etc..)
• Eastern Buddhism - Chinese transmission of Mahayana Buddhism (China, Korea, Japan etc..)
• Northern Buddhism - heir of late Indian forms where Vajrayana forms dominate (Tibet, Mongolia, Some Russian areas etc..)

I think the model works for describing the major schools of Buddhism today in a way which doesn't have any derogatory overtones

I don't think there is one commonly-accepted alternative name, but I did find some interesting suggestions here. Of all the listed suggestions IMHO these three are best:

• Nikāya Buddhism; coined by Professor Masatoshi Nagatomi of Harvard University especially for the purpose of avoiding the use of the term Hinayana
• Non-Mahayana Buddhism
• Early Buddhism

As I was just explaining in a comment to one of my answers, the term "Hinayana" is widely used by Tibetan Buddhism teachers to refer to basic/elementary/foundational (and because of this often simplified) aspects of Buddha-Dharma. If you'd go to their lectures, you'd hear this notion of Hinayana-understanding vs. Mahayana-understanding discussed in almost every other lecture. Amongst tens of books written by the teacher I consider my Root Guru, Chogyam Trungpa Rinpoche, a recently published 3-volume set has its first book, of 680 pages, dedicated to Hinayana, with this word used on almost every page.

Again, to emphasize, "Hinayana" is not used to refer to Theravada at all. Rather, it is used in two senses: one, to refer to a primitive interpretation of Buddha-Dharma (by a member of any school, and of any standing, but usually a beginner, or a "senior junior") and two, to refer to the first phase of Buddhist upbringing, during which the student is introduced to the most basic discipline and doctrines, that serve as the foundation for subsequent education & practice.

Imagine two teachers discussing their students with each other: "I have 3 Hinayana-level students, 2 Mahayana-level, and 1 Mahamudra" or "This guy is stuck at Hinayana level, perhaps I should try Kriyayogatantra..."

Whoever thinks the term is derogatory misses the point. The term is indeed used to refer to "primitive" or "elementary" level of Dharma. But we don't consider "elementary education" a derogatory term, do we? Or perhaps, in countries where Parliament comes in two houses, we don't consider The Lower House of Parliament a derogatory term? And when the rental cars come in three classes: economy, business and luxury -- we do not insist that the use of the term "economy" should be discouraged because it hurts the feelings of lower-income people etc.

The term "Hinayana" is an important term, used by thousands of gurus over thousands of years to teach their students a very important point: that Dharma, like any other non-trivial area of human activity goes far beyond simple logic, and requires depth, sensitivity, ability to compromise, to go beyond black-and-white view of the world, to juggle multiple contradicting needs, to understand different perspectives, and in general to not get stuck at the level of mechanical application of formulaic if-then-else rules.

Besides the negative connotations ("black-n-white understanding of the beginner"), the way it was presented by Chogyam Trungpa Rinpoche I feel "hinayana" also has positive connotations like "fundamental basic teaching" and "spartan discipline".

Here's how Trungpa praised hinayana in his famous short talk, Never Forget Hinayana (edited for readability):

Good evening. Ladies and gentlemen, it is a very profound time and profound experience for us to realize how important is the hinayana teaching.

The hinayana teaching should not be regarded as something that you can just carry out and then get rid of, or discard. The hinayana teaching is the life force that carries our practice and discipline, which goes on continuously. From that point of view the hinayana should be regarded as life’s strength.

It is [important] for us to understand that basic life [force], that basic strength. It is very important to us, and inseparable from our lives and our existence as individuals. It is the life force that carries [you] on whether you are going through the hinayana, mahayana, or vajrayana [levels]. It is our substance and our sustenance.

NEVER FORGET HINAYANA!