Ok - After trial and error - figured it out:
In the helper function:
Template.tableBox.table = function(tableID){
return Rolls.find({"Roll.tableName": tableID});
}
I needed to add the nested Roll.tableName property name but within brackets as the query.
And back in the tableBox template:
<template name="tableBox">
<table id="{{name}}" class="table table-condensed table-striped">
<tr>
<td>{{name}}</td>
<td> Min:</td>
<td>{{minBet}}</td>
<td>{{cPlayers}}</td>
</tr>
<tr>
<td>Dice1</td>
<td>Dice2</td>
<td>Dice3</td>
<td>Total</td>
</tr>
{{#each table name}}
{{> tableRow}}
{{/each}}
</table>
</template>
No need for the curly braces for the 'Name' argument for the function. Somehow handlebars and Meteor recognise the context you are referring to without the curly braces and applies it like it is within {{name}} for the tableBox. I.e. "T1", "T2", "T3" are passed correctly to the function and now my unique tables only contain the list of rolls specific to individual tables.