Looping on the User Field added to Entry

You are setting variables within the scope of the for loop – they only exist there. You can fix this by setting up empty variables before the loop, like:

{% set webinar = block.webinar.all() %}
{% if webinar is not empty %}
    {% for entry in webinar %}

        {# Setup empty variables #}

        {% set name = null %}
        {% set avatar = null %}
        {% set job = null %}
        {% set linkedin = null %}

        {% set url = entry.url %}
        {% set title = entry.title %}
        {% set desc = entry.previewDescription %}
        {% set img = entry.previewImage.one() %}   

        {% for expert in entry.eventHost %}
            {% set name = expert.name %}
            {% set avatar = expert.avatar %}
            {% set job = expert.personJobTitle %}
            {% if expert.linkedInProfile %}
                {% set linkedin = expert.linkedInProfile.url %}
            {% endif %}
        {% endfor %}

        {{ title }}
        {{ name }}
        {{ job }}

    {% endfor %}
{% endif %}

Or in one line, for neatness:

{% set name, avatar, job, linkedin = null, null, null, null %}

This one has got me many times ;)