Hi Jean,
This might be a bit tenuous and this subject is very much yours rather than mine, but the term oroshigane can have the meaning "blown steel" so maybe a reference to him using this process rather than a tatara to make his steel? From an article by Markus Sesko:
"At this point, you may ask yourself, what does the very term oroshigane actually mean. I mean, gane is clear, it means “steel”, but oroshi? In our case, the term oroshi is assumed to come from the term fuki-orosu (吹き下す) which means “blow down upon,” and was probably chosen because it resembles the way the smith blows air into the prepared steel/charcoal arrangement for the oroshigane process in his furnace. Strong and dangerous winds blowing down the slope of a mountain are referred to as oroshi as well, written with the character (颪), which has to be taken literally so to speak, i.e. “down” (下) and “wind” (風)."
https://markussesko.com/2018/09/30/oroshigane-mentioned-in-signatures/