I know that we can use the entity numbers ₹ and ₹ to display an Indian rupee symbol(₹). But as the pound has entity name £, the yen has ¥, is there any special name like &rupee; to be used to display this symbol?
I came to know that there's none, can anyone suggest how can we apply to the w3 community to add that specific character to the list and apply it's usage
As I understand it, there is no process for getting a new named reference in HTML. That means, you won't get &rupee; or &emoji-train; or similar.
HTML5 entity names are all listed at https://www.w3.org/TR/html/syntax.html#named-character-references
They are derived from the XML entity names https://www.w3.org/TR/xml-entity-names/
The preferred way of referencing characters is using their decimal or hexidecimal reference. In this case ₹ or ₹.
This is because an older browser may not know what to do with &rupee; - but will always know how to look up a numeric reference in a font table.
The easiest way is just to paste in the ₹ symbol directly.