Resume Question: Private Credit at MF PE Subsidiary

I need an honest opinion on this dilemma I'm in.

I signed summer 2024 for IB at a MM firm and am hoping to lateral to a BB or EB.

This summer, I'm interning at a direct lending firm that is one of many originators within the private credit platform of a MF PE firm.

I know this is a bit of a stretch, but I was wondering if putting the MF PE firm as my employer on my resume would pass the straight face test. In the description portion, I would, of course, clarify that I worked for x group at the private credit firm.

I'm only asking this because I know how hard it is to lateral in this environment, and I want to market myself as well as possible. I feel like I can get a lot more looks if my resume has a well-known PE firm at the top of it than less well known direct lending firm.