The root HWH is attested in Aramaic at least since
the eighth century (KAI) with the same meaning as the
biblical HYH. In fact a few cases of the Aramaic form
are preserved in the HB, compared with thousands of
cases of the standard HYH. With the exception of the
medial consonant, they are quite similar.
Therefore I am at a complete loss to understand
when you state:
"..... And continuing the line of uncertainty, we do
not know whether there is a wordplay (similarity of sounds)
between the use of HYH in Exodus 3:14 and the name
YHWH in 3:15. We do not even have any clues that could
suggest that there was a connection between the verb HYH
and YHWH."