[рони]

noname122,
не проверял, но логика примерно такая ...

function validate(mF) {

            myForm = mF;

            var ima = textValid(myForm.ima.value, myForm.vIma);
            var fam = textValid(myForm.family.value, myForm.vFam);
            var login = loginValid(myForm.login.value);
            var pass = passValid(myForm.pass1.value);
            var people = JSON.parse(window.localStorage.getItem("people") || "[]");
            if (ima && fam && login && pass) {
                var i = myForm.ima.value,
                    f = myForm.family.value;
                var index = people.findIndex(a => a.i == i && a.f == f);
                if (index == -1) {
                    alert("о новенький!");
                    people.push({
                        i,
                        f
                    });
                    window.localStorage.setItem("people", JSON.stringify(people))
                } else {
                    alert(`Привет ${i} ${f}`);
                }

            }
            return ima && fam && login && pass;
        }