I wanted to do this post just to sum-up what we know and don't know about Kurosaki Isshin.
What we know
1. He is a captain level shinigami
2. His captain haori is draped over one shoulder and pinned with a bit of metal
3. He knows Urahara Kisuke and Urahara's comment's about any drop in Isshin's reiatsu being his fault might mean the Urahara was the one to either help him regain his power or most likely, was the one who helped him abandon his shinigami form.
4. He knows Ishida Ryuken and Isshin are friends. Probably the same kind of friends Ishida Uryuu and Ichigo are. I.e. good friends who are very similar to each other but who constantly fight and pretend to be enemies.
5. No one in Soul Society has commented on Ichigo's last name
6. Rukia didn't recognise him but it is unclear if any other shinigami has seen Isshin
7. Shinji didn't recognise Isshin's reiatsu
8. He abandoned his Shinigami form 20 years ago
9. He, like Ishida, is a doctor.
What we don't know
1. If he was Gotei 13 or Royal Guard
2. If Gotei 13, what squad he was part off
3. When exactly did he leave Soul Society (he abandoned his shinigami form 20 years ago, that doesn't have to be when he left)
4. Why he left (romantic version says he left for the sake of Masaki but frankly we don't know)
5. Why no one is recognising Ichigo's last name
What fans think
Here I am only going to state theories that are possible. I know there are other theories but I don't care to repeat idiotic crack theories that are not remotely plausible when you just stop to think about it. Not that I am saying that any theory I didn't list below is idiotic and crack, the theories listed below are the ones I have heard that didn't appear to be an utter load of bullshit.
1. Isshin was a captain of Gotei 13 and changed his last-name when he married Masaki, this is actually a not uncommon practice in Asia but only recently coming into vogue in the west. Traditionally, the person with the more powerful/prominent family got to keep their name and their spouse changed their name. Also, if the husband was going to move in with the wife's family/clan they also took the wife's name. So not an uncommon thing to happen.
2. Isshin was a captain of the Gotei 13 but no one has made the connection because of the altered context. It's amazing how easy it is to fool people by altering the context. The example most people would be familiar with is Superman being able to hide his identity by just wearing glasses. It's not so much the glasses that hid his identity but the fact that the context of existences was so different between those two. I.e. people in Soul Society have a hard time picturing one of their captains living in the living world, married with kids and working as a doctor.
3. Isshin was a captin of the Gotei 13 but Rukia doesn't recognise him because captains are known by name but not necessarily by sight by rank and file soldiers. This is sort of a weak argument because Renji asked who Matsumoto's captain was in page. But I think it was more Renji wasn't sure which squad's vice-captain Matsumoto was then not knowing who the captain of squad 10 was.
4. If Isshin was Gotei 13, he was most likely the captain of squad 10. Squad 10 didn't have a captain 100 years ago, it is explicitly stated that captain had died in the line of duty and we aren't sure when Hitsugaya became captain but it is mostly likely within the last 10 years.
5. Isshin was a royal guard, which neatly explains why no one knows him. Although Yama-jii probably does but Yama-jii has been very busy and isn't all that communicative so...
There are also couple of theories for Masaki, Ichigo's mother, not being an ordinary human. It is speculated that she is either a quincy or a shinigami herself. Only real proof there is that Masaki wasn't just any human is that grandfisher was satisfied with just her soul. Think about it, if she was just a normal human, why would grand fisher leave after eating her when Ichigo was just lying under her body. I mean, even as a child Ichigo had high reiatsu. So even as a child Grandfisher would prefer Ichigo's soul over Masaki's if Masaki was just a human and Ichigo wasn't. Also, in the manga grand fisher prefered the soul of children so it does make me wonder exactly how Ichigo survived that day and what Masaki did to drive grand fisher away.
Lastly, I wanted to address a recent theory about Isshin that's getting a fair bit of mention recently. I am talking about the theory that says, Isshin might have some connection to the Shiba's, who did used to be the fifth noble house but were demoted. Thing is this is based on Ichigo having a passing resemblance to Shiba Kaien. However, I personally don't think Ichigo looks so much like Kaien that it justifies a blood connection (or even a reincarnation theory) and also we don't know when they were expelled and why. Also, you would have expected one of the Shiba's to say something but as it is, neither Shiba seemed to see the resemblance between Kaien and Ichigo. It's only Byakuya, Ukitake and Rukia who made the connection and I got the impression it was a combination of looks and personality that made them think that. Also, there is no hint that another Shiba who was the captain of squad x disappeared on Soul Society. So I don't think this theory has much ground to stand on and I am kind of hoping it will go away before it becomes another thing that get's continuously brought up and forcing others to continuously explain why it is highly unlikely.
Anyway, just wanted to make this post as "Isshin theories" seems to be all the rage these days.
Will Chapter 407 provide answers?
So what's the chances that chapter 407 will provide answers? Well, firstly, we finished chapter 406 with Isshin telling Ichigo to open a Senkaimon. There is no evidence that Ichigo CAN open a Senkaimon. He saw Renji do it once but that's about it. Not that I don't think Isshin doesn't know how to open a Senkaimon. I imagine ordering Ichigo to do the opening is a instinctive reaction because Isshin's a captain and captains just don't do these kinds of plebeian things. ^.^ So here is the thing, we left chapter 405 with Rangiku running towards the location of Gin. Gin's gone but in the spot he used to be is Ichigo and Isshin. So there is a good chance in chapter 407, Rangiku will arrive and come face to face with Isshin. It also seems that Kubo had her up and running so she could open the Senkaimon. Maybe she'll cross to Soul Society with them, maybe she won't but I am about 90% certain that she'll end-up opening the Senkaimon.
But back to Isshin. So Isshin comes face to face with Rangiku, what then? Will she recognise him? Will she call him by his real name assuming that Kurosaki is an assumed name? If she does recognise him, that'll pretty much settle that Isshin was a Gotei 13 captain and most like (and Rangiku might even confirm this) captain of Squad 10. If she does recognise him and calls him by a different name to "Kurosaki", that'll settle the whole "Shiba" theory once and for all too! Whichever way, I can't wait for chapter 407!