There’s a lot of those. My recollection is these were in use at Brigham and Womens. They were co-developing a hospital app with Beth Israel. There was a lot of inter-cooperation in the Boston area medical centers, can’t say for sure where I encountered a 7 Dwarves named machine. Could have been more than one of them. Whimsical naming was common then. You could tell something about the people you’d be working with based on their machine names. If they were names like “A”, “B”,“C”… it didn’t look promising.
I believe the workstations in the University of Texas CCWF Sun lab (I can’t remember what CCWF stood for, or if that is even the right acronym) were named for the seven dwarves, among other things. I also don’t remember which of the dwarves were 68000 and which were sparc based, but that was always a fun balance. The sparc ones were faster, but also more heavily used.
I’m sure naming after the seven dwarves was not unique to UT in 1990.
To keep this mildly on topic, many a copyright infringement was performed on those computers; primarily on Usenet binary groups.
I guess the point is, if the server names (or apps) are internal to the company and unlikely to appear in the press generally and be known to the public - nobody cares. I suppose the thing would be if it became a more public thing - such as your internal sports team winning the state business league championship and being all over the news, then there might be an issue. But team names like “Rangers” or “Bulls” or “Browns” or “Eagles” are perhaps fairly generic. “fighting Irish” less so.