If memory serves me correct, Office up until version 2013 allow for primary plus secondary installation by same user (that is, primary installation onto desktop, secondary onto a laptop), using same product key (that's the way I am using my 2010 version).
This policy got abandoned in 2016 version, so if this is the version OP is using, he/she must acquire separate license (whether 2016 or 365) for the Surface.