What's the most appropriate name for this reaction?
As Koch's reaction (Gatterman-Koch Formylation) adds a carbonyl group, and not a carboxylic acid group, I decide to go with Kolbe's reaction.


You started right, and then took the wrong turn ;-)

Under acidic conditions


the proton adds to the $\ce{C=C}$ double bond and gives a secondary cation
the cation reacts with carbon monoxide and yields an acylium cation
the latter reacts with water to result in the formation of a carboxylic acid


The whole process is known as the Koch reaction (without the Gattermann).