Find entries related to user and display field name
What could work for you is to get the events for each field separatly:

{% set firstEvents = craft.entries.section('events').relatedTo({
    element: user,
    field: 'firstEntriesField'
}) %}

{% set secondEvents = craft.entries.section('events').relatedTo({
    element: user,
    field: 'secondEntriesField'
}) %}


If you need them combined in one loop, I can't think of another way other than to query x + 1 times:

{% set allEvents = craft.entries.section('events').relatedTo({
    element: user,
}) %}

{% set firstEventsIds = craft.entries.section('events').relatedTo({
    element: user,
    field: 'firstEntriesField'
}).ids() %}

{% set secondEventsIds = craft.entries.section('events').relatedTo({
    element: user,
    field: 'secondEntriesField'
}).ids() %}

{% for event in allEvents %}
    {% if event.id in firstEventsIds %}
        {# Event related through firstEntriesField #}
    {% elseif event.id in secondEventsIds %}
        {# Event related through secondEntriesField #}
    {% endif %}
{% endfor %}