Laravel You requested 1 items, but there are only 0 items available

Use inRandomOrder() instead:

$physician = SelectOption::where('select_option_group_id', 1)->inRandomOrder()->first();
$name = is_null($physician) ? 'No data available' : $physician->name;

Check if collection is not empty prior doing random():

$collection = SelectOption::where('select_option_group_id', 1)->pluck('name');
if (!$collection->isEmpty()) {
    $physician = $collection->random();
} else {
    ...
}