How to make axios synchronous

You can't (or at least really shouldn't) make it synchronous, so you'll need a different way forward.

One idea: return the promise from Axios:

checkUniqueness () {
    return axios.get('/api/persons/unique/alias', {
        params: {
            id: this.id,
            alias: this.alias,
        }
    })
    .then((response) => {
        console.log('2. server response:' + response.data.unique)
        this.valid = response.data.unique;
    });
}

and then call then() on it in save():

this.checkUniqueness()
.then((returnVal) => {
   // other validations here
  //  save
})
.catch(err => console.log("Axios err: ", err))

You could even do all your checking on one place if you returned the value from Axios's then() rather than setting the flag:

.then((response) => {
    console.log('2. server response:' + response.data.unique)
    return response.data.unique;
 });

then in save:

this.checkUniqueness()
.then((valid) => {
    if (valid) // do something
   // other validations here
   //  save
})

If you just do what JS docs (mozilla) show you can treat Axios as just another promise. Be careful about making the request synchronous bc it can freeze the UI and the rest of your app.

       async save () {
            this.valid = true;
            console.log('before checking');

            const isUnique = await this.checkUniqueness();
            console.log(isUnique); // => value waited for and returned from this.checkUniqueness()
            // other validations here

            if (this.valid) {
                console.log('3. checked valid, can save now');
                // save now
            }
        }

axios.get(...) returns a promise (a task that is promised for later) and you can wait the interpreter untill this promise ends with an await word in ES6+ :

let response = await axios.get(...)

but axios.get(...) returns the response while axios.get(...).then(...) returns what you intended to return. so if you dont return anything in then part it will be undefined:

let response = await axios.get(...).then() // nothing returns in then
console.log(response) // undefined