Can you teleport a player to a certain block without specifying the coordinates?

yes it is. however it requires setup. there is no command in the game that allows you to do something like this but we have function files in minecraft. if you already have a command that teleports you there you can make a function file with that teleport command in it and when you run it via /function you will teleport.

however this requires a lot of time and effort to compared to copying the command from a notepad and only shaves off a few characters from the command.

however if you do want to attempt it 3rd party documentation for minecraft behaviour is available here

You can teleport players to entities and armor stands are entities so they're good markers for this purpose. Place an armor stand and name it with a name tag (such as 'pos1'). Then you can teleport the player to the armor stand with the following command.

/tp @p @e[name=pos1]

If you want to move the armor stand without having to replace and rename it, you can teleport the armor stand to your current position.

/tp @e[name=pos1] @p

If you don't want the armor stand to be visible you can grant the armor stand an invisibility effect with particles disabled for a really long time.

/effect @e[name=pos1] invisibility 99999999 0 true

If you wish to remove the armor stands you can kill them easily with commands

/kill @e[name=pos1]

There are limits to this method. Armor stands far outside render distance won't be picked up by the selector. For the default 48 chunk render distance that's in my tests it was something like 870 blocks or so which is pretty far. If you need more than that you can resort to adding /tickingarea