SIM card contacts take time to load after turning phone on Device: MMX A89
Android: 4.0.4 Ice Cream Sandwich

Whenever I switch off the phone, then switch it on, SIM card contacts takes a long time to load. They don't load properly. In the call list, only phone numbers are shown and not the names associated with them.

How can I fix this problem?
That's normal behaviour for the SIM card phone book, not just for Android, but on older dumbphones too. I remember my old Nokia 3310 took about a minute after booting before the phone book (and other SIM card functions) became available. The problem wasn't really noticeable on early Android phones because they took so long to boot anyway. While the phones are a lot quicker now, the SIM cards are still the same old technology.

If you want to get at them more quickly, either leave your phone turned on, or copy them to the device.