How to Report a wrong street name in Spain?

Your phrase "the location marks it in a different place because the street has another name" make me wonder if really the place is mapped wrongly (in which case the previous answers show you how to fix that) or if you are setting a marker on top of the map using some address look up service. If the latter is the case there might be an error coming from the lookup service or it might be a matter of how to formulate the request to that service.

If you link to your website we could have a look at what might be the problem.

There are two main options: you can leave a note (wiki) or you can edit the map yourself: there's a Beginners' guide on the Wiki or you can go to osm.org, look for the city where the park should be, click on "Edit" in the top left and add it (the default editor will prompt a little tutorial to let you know how to make your first edits, then you are ready to edit the map).

You can add a note to the map at the relevant location https://wiki.openstreetmap.org/wiki/ES:Notas

Hopefully an OpenStreetMap user will see the note and make the change, but note that we are all volunteers and there is no guarantee that there are active mappers in your area. It helps to add as many details as possible to the note so that other mappers can be confident the change is correct, e.g. is the correct name visible on street signs or on a map/callejero provided by the Ayuntamiento, was the name changed recently etc.

If you want to guarantee the change is made, you can edit OpenStreetMap yourself. Changing a name on an object that is already mapped is quite easy. More info at https://wiki.openstreetmap.org/wiki/ES:Gu%C3%ADa_de_principiantes

(Edit: I was typing as Mannivu was posting, hence the duplicate information)

Login at https://www.openstreetmap.org/login

Point the area

Once you are close enough, zoom until OSM elements appear

click "Edit" button in the upper left corner and "Edit with iD"; the url should change to something like https://www.openstreetmap.org/edit?editor=id#map=19/40.52847/-5.19783

clicking the way you want to rename and find the name tag in the form on the left, correct it and upload clicking the button on the upper left corner (or by shortcut CTRL-S)