You can say "sorfear" which is used for surf the net, or "surfear" which is used for surf (the sport).
I do not think it is an official word, but Spain is the only country which can indeed make it official, whether they accept it; is up to them. Since those are words adapted from the English language, they may take time to be accepted. However, they eventually just accept them if enough people are using them or they may just name them as "slangs" for whatever the word they officially associate with it.
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