"Tomiki Aikido" is a misnomer. However, keep on reading.
Tomiki started teaching his system of learning/teaching Aikido before naming it. Thus, people (especially in the USA) started to call it "Tomiki Aikido" because it came from Tomiki. Afterwards, Tomiki (with others such as Oba and Nariyama) continue to refine his system. He called it the Shodokan Aikido randori system in the inaugural address at the opening of Shodokan. Tomiki was not arrogant enough to name his style by his own name. Thus, the real name of the style is Shodokan Aikido.
However, people keep using "Tomiki Aikido" and more often than not, what they teach is the first version (or unrefined version) of the Shodokan Aikido randori system. The two are close but have differences but that is a topic for another time.
Aikido, being the "way of harmony", has so much harmony in it that everyone is creating their own organisation⸮ All start to deviate from the Shodokan Aikido randori system. Sometimes, this is both justified and wanted (see 守破離 - Shuhari). Sometimes, it is ego, pride, and hubris.
The two main Japanese organisation are the JAA headed by Shishida-shihan and SAF headed by Nariyama-shihan. The latter used to be the head technical director of the JAA but there was a split due to politics I have no intentions to get into and are not interesting to anyone. Most, if not all, organisation in the world tend to follow either one of these two.
In the UK, the situation is crazy: everyone is starting their own organisation, whether either as part of the overall umbrella Aikido organisation (the BAB) or against it as it is the tool to the Devil™ or some such. Note that this is in no way limited to Shodokan/Sport Aikido. Traditional is even worst if anything.
I strongly suspect that this crazy is the same in the USA, and any other country in the world…
Let's look at the kanji:
- 昭道館 for Shōdōkan
- 松濤館 for Shōtōkan
Notice that the first two kanji are different… And that's where I get stuck as I do not read Japanese. As far as I know, 昭道館 (Shodokan) can be translated as "open way". This is something Tomiki was very keen on: he wanted anyone who knew his system to teach it to anyone who asked, whatever their race, creed, or gender.
I asked about the meaning of 昭道館 vs 松濤館 on Japanese Language and this answer provided the insight:
Both styles are named after the dojo where they originated. The 館 ("kan") in both names means a type of building and is commonly suffixed to the names of dojos.
Please see the full answer for details.
Mostly, this comes from conversations, books, and videos of Tomiki, Nariyama, Phil Newcombe and Scott Allbright. Nariyama has written a few books with good history sections. Aikido and Randori: Reconciliation of Two Opposing Forces has Scott Allbright's views and contain lots of his experience talking to Tomiki.