Yes, there is no key included with the Surface 3 package. To get the 1 year of Office 365 Personal, you just tap the Orange Office 365 tile and then sign in to assign the 1 year to the account. This really should've been explained with a sheet of some sort in the packaging. I had to go back to the Microsoft Store for the explanation.
Office 365 Home is the 5 installations and Office 365 Personal is 1 installation.
seremify is correct about "converting".
PDevil is incorrect about forfeiture. I learned this the hard way. I purchased 2 licenses of Office 365 Home so i could get 10 installations for 1 year. However, I applied them both to one Microsoft account and rather than allow me 10 installations for 1 year, it simply stacked them so I still had 5 installations but for 2 years. This wasn't the behavior I wanted, and I went through many sessions with Microsoft Support to fix the problem. Currently, they do not allow what I was trying to do. I had to assign each subscription to a different Microsoft account in order to achieve 10 installations for 1 year rather than stacking.
So you can stack subscriptions. There is no forfeiting a year if you apply a different license while a subscription is active. It will stack. If you want it to stack, then simply apply the new code. If you do not want them to stack, you will need to assign the second subscription code to a separate Microsoft account. Again, this doesn't apply to the Surface 3 situation because there is no code with the Surface 3.