Hi Jorgen.
Autocomplete can be turned on as I said above and then the second time would have the string, however since it is capturing data everywhere it quickly becomes clutered with other strings than your names in InfoPath. There is no way to control when and where it is activated.
If you use a dropdown list of names then you can use the keyboard to jump to the first letter. Example you click on the drop down and type "T" it would move through the list to the entries begining with T.
A true autocomplete must be done in code or you can use some other logic such as begins with but there is nothing built in. If your list is long, then there may be a way to use other meta data to reduce the list, select group first and then have your selection reduce to just that group.