I think that building custom no-brand desktops is a pretty acceptable cost cutting measure taken by some companies, so you could pitch it something like “we’re working with a company to build custom laptops exactly for what we need”, or if someone asks about it you can explain it ala “yes, we couldn’t get exactly what we needed so we build a completely custom fleet of laptops”.

Or ideal scenario, with a brand delete you slap a [company] sticker on it and nobody really notices that it’s not a Dell Latitude running Linux.