Gst Registration

in case of online service provider inter state gst registration is mandatory. you require separate registration.

No need to registered in Rajasthan , even though it's online services .

As per Section 22 Of The ACT Reads As 'Every Supplier Shall Be Liable To Be Registered Under This Act In The State Or Union Territory, Other Than Special Category States, From Where He Makes A Taxable Supply Of Goods Or Services Or Both, If His Aggregate Turnover In A Financial Year Exceeds Twenty Lakh Rupees, Provided That Where Such Person Makes Taxable Supplies Of Goods Or Services Or Both From Any Of The Special Category States, He Shall Be Liable To Be Registered If His Aggregate Turnover In A Financial Year Exceeds Ten Lakh Rupees.'

"PLEASE NOTE FROM WHERE....MEANS WHERE HE IS REGISTERED"

So in your case if your registered in Delhi you supply services from Delhi to Rajasthan by changing IGST