Hello aadit,
While registering for gst online as sole proprietor then they asked for legal name of business. In that case you only have to fill ur name as per pan card in that field and after generation of TRN i.e. temporary registration number they asked for trade name of business then you have to fill ur trade name in that field.
Further no other consequence of trade name in income tax as it will be filled in ur name.
Further when you want to convert sole proprietorship into LLC you will need new gst no

The income tax question is a separate question and asked in general.
Thanks