Use LINQ:
var strs = savefile.Select(a => Path.GetFileName(a)).ToArray();
Looking at the suggestion of minitech:
As long as you get the array of type FileInfo[] there is no need to convert it to string array. Just set the property DisplayMember to the property name you want to display in your ComboBox.
FileInfo[] savefile = new DirectoryInfo(mcsdir).GetFiles("*.bin");
comboBox1.DisplayMember = "Name";
comboBox1.DataSource = savefile;
Using this you keep your original FileInfo[] array with all additional information (as to the full path to your files) and same time display only the short filenames (without path) in your control.
(I assume that your question is about WinForms. If you are using Silverlight or WPF you need to set the property using the "Target" attribute).