Be default, GoldMine will search on Contact Name when the Search Center is activated (from the "Search" button on the top-hand toolbar).
We can change this behavior by;
1. Select Tools | Options from the top level menu.
2. Select the Lookup tab.
3. In this window, set your "Default lookup by field" to either Contact, Company or Remember Lookup By.
4. OK your way out.
I have mine set to "Remember Lookup By". That way, if I am searching for, say, Lastname, the search center will come up, ready to search by the Lastname every time I activate it.
Remember, searching for Contact Records in GoldMine one of the most important things you will ever do!