“Attempts” would be the most formally correct. “Tries” sounds natural to my native US English ears. 😆 “Goes” doesn’t sound natural in this sentence. A variation of “goes” that can be used to represent a “try” or “attempt” is included in the common phrase is “give it a go” (“give it a try”).

You have only three ATTEMPTS to type in your identity number

For an American "tries" would be clear, but in a business context, say, "attempts" is better. We also frequently say we'll give something new "a go," but only very informally. "Haven't had this food, but I'll give it a go." Or a new sport, or skill.

Attempts