I guess the question is does anyone even care about corp membership and what shows up on the ticker? I'd still be 'me' just with a different corp name.
I completely get the way you're feeling here. Corp membership does affect character identity IMO. I'm in a similar situation to you, in that I have two Sansha-aligned characters who are both in the same Sansha-loyalist alliance, but neither of them are members of the by far dominant corporation (True Slave Foundations) within the alliance. Katla is still a member of the for all practical purposes derelict Naqam, while Ruby is in her own little one-person corp, Tomorrowland Orphanage.
Now, Katla would not really be an ideal fit for TS-F, and there's no real practical reason she should be, at least unless the TS-F leadership should decide to trim the ranks and cut Naqam free from the alliance. Ruby on the other hand, probably would be a good fit, and it would have practical benefits since she shares a base with TS-F, participates in roams, etc. And there's no real reason I couldn't still keep the orphanage in operation as a pure RP construct. It is something I have considered, and it might happen someday. But it would still feel weird and a bit sad to give up the one-man corp she's been in for pretty much the whole of her career.
I should mention that unlike in your case, I have had zero prodding, nagging or eye-rolling from any of the other alliance people about my special snowflake ways, and I absolutely love them for that.
So yeah, bottom line - if this change would make you uncomfortable, stick to Nobilita Nera. It sounds like you're doing great with Silas as it is.