The following process for installing and naming SIM cards in a Dual SIM phone helped me to identify SIMs clearly and quickly at all times. This refers to a use case when you want to use one SIM for mobile data and the other for phone calls. You may have to adapt that to your use case.
Place your data SIM into the SIM 1 slot. Insert the SIM tray into the phone.
Give your data SIM a SIM name "SIM1 Network-Name Data" in the Android settings. Obviously, change "Network-Name" to the name of your network operator, such as "O2" or "T-Mobile".
Place your phone SIM into the SIM 2 slot. Insert the SIM tray into the phone.
Give your phone SIM a SIM name "SIM2 Network-Name Phone" in the Android settings.
Why and how this helps
By inserting and naming one SIM card after the other in a two-step process, it becomes easy to identify which of the two SIM cards is which in Android, even if both SIM cards are for the same mobile network.
After naming SIM cards, you can in principle swap them in the SIM tray. The SIM names refer to the SIM cards and not the SIM slots, so swapping cards will change the icon position and position in the SIM card list, but will have no effect on the SIM card configurations. So after the initial setup, it would be easiest to always and only identify your SIM card by name in Android, forgetting about which card is in which slot. However, that is not recommendable because there is one exception that requires us to know which SIM card is SIM 1 and which is SIM 2: the signal strength icons in the status bar only use positions (SIM 1 left, SIM 2 right), not SIM names. Due to this, it is best to simply include the SIM number at the start of your SIM name (e.g. "SIM1 O2"). That also makes it clear that SIMs are ordered by SIM number in the SIM list, which is otherwise not obvious.
In addition, it is best to put the SIM used for data connections into the SIM 1 slot. This is because otherwise you'll be confused when trying to figure out to which SIM a single connection type identifier ("4G", "3G" etc.) refers when it appears in between the two signal strength icons in the status bar. The connection type identifier always refers to the icon following it, but you will forget that. Placing the data SIM into the SIM 1 slot makes it unnecessary to remember this, as the connection type identifier icon will then appear before the first icon, evidently referring to that first icon and not the second.
In addition, it can be a good idea to include the ending digits of the SIM card numbers in the Android SIM names, for example "SIM1 O2 Data #…5481. That makes it possible to make sure the SIM cards are in the trays they should be, even if both come from the same network operator. It also tells you which physical SIM card is meant for which use, without having to consult other notes in or out of the phone.