When I am traveling abroad, I use a different SIM card in my iPhone, but when I put in the new SIM, the recipients of messages within existing, and new, iMessage conversations, see the travel SIM card phone number, and my own incoming messages are split so I see a new conversation from someone elses' phone number instead of their name as a contact.

I am trying to:

A) make sure all existing and new imessage conversations only see my regular SIM phone number, and not the phone number on the travel SIM card - and our conversation continues within the existing thread on both of our phones
B) when I message someone, or they message me, I see the conversation continue in the existing thread with their contact name, and not a new thread that shows their phone number

Is there any way to do this?

You cannot use a phone number for iMessage that is different than the active SIM.

You can use any email address that is tied to your Apple account. You can also choose whether you start new conversations from your current active phone number (which will change when you change SIMs) or one of your email addresses (which will remain constant) in Settings - Messages - Send & Receive.

There may be a way to do something like this with a phone number without using the phone number from an active SIM.

For example, using a Google Voice phone number: set all messages in GV app to forward to the SIM number. As the new text messages start coming into the iMessage app, they appear to come from weird unknown numbers. but which are Google's proxy numbers. Then you compare those new texts to the ones in GV app to see who they are from. You then save them from the iMessage app to the correct contact, with that proxy number assigned as a pager, to know which is the proxy number. After doing this, text back via iMessage and the other party gets the response from the GV number. It's a hassle to do it for all incoming new messages/contacts, but once it's done per contact, it is not a hassle with that contact again. It's a workaround, not a generally attractive one.

I don't think I'm tech savvy enough to pull this off, plus it sounds like a hassle. I will just use my google voice number to text people who I don't want to know that I'm abroad.

They still won't be iMessages, though - just regular texts. And you can't send SMS or imessage from any number besides the one on the active SIM using the Messages app.

What you can do is have multiple devices signed into the same Apple ID, so if you move the other SIM to an old iPhone, as long as it signs and registers then you can send and receive from that number of the other phone.

This might work with dual SIM iPhone as well but never tried that

It does work with Dual Sim. So long as that SIM is active... you can choose to originate messages from that number... even if you have Cellular data and voice using the other sim.

Best practices for iMessage is to set 'start new conversations from" to one of your Apple ID email address. In settings/Messages/Send & Receive. Yes, you can have more than one, you set that up elsewhere so you don't have to advertise your main email address if you don't want to.

That way any new conversations you start will work regardless of which SIM you have activated/installed.

From the remote sender's perspective, existing conversations using a number that isn't active may not work when you change SIMs or deactivate an eSIM. Eventually, doing this solves that. However does not solve for people that attempt to use your number to send a message. You can use the virtual number app from your provider to attempt to mitigate that, but only if the message reverts to SMS.

The other better mitigation for this is to use a provider that includes some form of world-wide service with messaging in your plan with a dual-sim device, so you can keep your main number active virtually world wide. I'm doing both these days. (initiate from email address + t-mobile us)

-David