Question: Probably, as people could not pronounce Vrshni, they pronounced it as Varshneya - as they made Gupt as Gupta and Sinh as Singh?
Answer: The spelling of Varshneya is correct as from Sanskrit, Meaning descendants of Vrshni. Before,during and after Krshniji times it is being used.Like Kaunteya meaning sons of Kunti. During recitation of Bhagwat Katha few dharma gurus quite often use this term.Guptaka used to be first name like Rajesh, Suresh. So Gupta were termed for descendants of Guptaka. Few of the descendants of King Ahivarn(Barnwals) were Guptak. Originator of Agarwals,according to one legend, may be Agresen living in Agroha, harayana just before kaliyug, who declared and followed Bania tradition (start of kaliyug was of great depression times which lasted for 1500 years or more, due to Mahabharata war), his wife was a Nagavanshi and having 18 sons, they are the main gotras of agarwals. Few of his descendants were Guptak. So over 3-4 millenniums Gupta are generally regarded as Banias.
This past century some Varshneys have started writing Gupta due to identification with Banias. Technically, it may not be wrong since 11th descendant of Abimanyu(son of Pandav Arjun) was Guptaka.
Gupta Empire was a term used by historains, where ShriGupt(one word) whose descendants mixed with Licchavi kul was the founder of the Gupta dynasty.