Hey, Thomas!
Changing the IC Service account password (ICAdmin) is a pain, so I always suggest taking steps to avoid it, if possible. As already mentioned, you will need to re-run Setup Assistant (this will run in component mode, so chose "Identity") on the IC Servers themselves (do NOT be tempted to manually change the password in the Services control panel).
In addition, any server where the IC Service account is used / referenced will need updating. Media Servers, SIP Proxies, CCSs (If you are a Dialer site) and so on. It is unlikely you will be able to do this with absolutely no service interruption (so plan for an outage) although if you have Switchover on your IC Servers (and CCSs, if present) as well as n+1 redundancy in your Media Servers (at each site) you might stand a chance.
My usual advice to my students is to exempt the IC Service account from password change policies. This, naturally, is a security concern, so I also recommend mitigating that by removing Interactive Login rights for the user. This, in turn, will cause problems if you routinely use the account for day to day administration of your system. I would therefore recommend that once you have the system installed, you create accounts for your support team and give them the IC Role of Administrator. From that point on, you administer the system using your own account, and not the IC Service account. This has the side benefit of having the audit logs correctly show who made what change. (Know who to hit when things go wrong!!!)
Along similar lines, while discussing this matter, I also strongly oppose the practice of opening an RDP session to the IC Server in order to run IA, Attendant etc. These are client applications and should be installed on your client machine and run from there! (If you are not sure how to do this, look at the shares published from the IC Server. There is one each containing the installs for Client (agent) apps (2 of these, 32 bit and 64 bit), Business Manager (Supervisor) apps and Server Manager (Administration) apps. It's the last of these that you need.)
Anyway, I hope this helps. Probably more than you initially thought you needed to know, but hopefully enough to enable you to meet you ongoing needs in an efficient manner!