Firstly, this is a player who prefers a particular play style
he's only playing along in the story so he can get to the next combat encounter
Is there a name for this kind of player?
There is no need to generalize this situation by attaching a label "this kind of player". It is not about being a specific kind of player, it is about playing a specific play style.
There is a particular play style indeed when PCs goes from one combat encounter to another. It's called "Hack and Slash" in the Dungeon Master's Guide. See DMG page 34, "Play style":
Hack and Slash
This style of play is straightforward, fun, exciting, and action-oriented. The players spend relatively little time developing personas for their characters, roleplaying noncombat situations, or discussing anything other than the immediate dangers of the dungeon.
Character motivation need be no more developed than a desire to kill monsters and acquire treasure.
Other sources (Mattew Mercer from the Critical Role, for instance) calls it the "Diablo-style". It is perfectly fine playing like that so far as all the participants are having fun.
Another thing that is also fine and well-known in the TRPG world is:
absolutely wants to be the one dishing out the most damage
This aspect — crafting a game character to make them excel at one particular role (damage dealing, in this case) — is called optimization:
Character optimization (aka CharOp, Char-Op) is the process of crafting a game character using the rules to make them excel at some given role.
A particular way of doing this is "min-maxing":
The practice of playing a role-playing game, wargame or video game with the intent of creating the "best" character by means of minimizing undesired or unimportant traits and maximizing desired ones. This is usually accomplished by improving one specific trait or ability
Such a player should be called "a player who currently prefers Hack and Slash play style" or "a combat-oriented min-maxer". If it causes troubles, this player is also "a player who is not on the same page with the rest of the group". The group itself could call him/her "a powergamer" (though powergaming not necessary assumes combat):
Powergaming (or power gaming) is a style of interacting with games or game-like systems, particularly video games, boardgames, and role-playing games, with the aim of maximizing progress towards a specific goal, to the exclusion of other considerations such as storytelling, atmosphere and camaraderie.
The "specific goal", in this case, is damage dealing.
If such a player comes into a group where some people (including the DM) do not enjoy this particular play style, him/her expectations will be failed. He will either adapt or leave the group, sooner or later.