No, but it would have been a move from the research division to the applications division at the time. This is around ten years ago, between Atari (pre-Google acquisition) and AlphaGo (post-Google acquisition), so I am unsure exactly what the effect would have been inside the organisation. But, if it was bad enough for people to want to leave I suspect it can not just have been about the label.

I should emphasise that DeepMind (based in London and having a very large degree of independence until the merger in 2023) and Google DeepMind (remember now that Google's research labs across the globe got merged into this entity, including the one in London that was previously split from DeepMind "proper", so it can be hard to tell at times what one means by "DeepMind") has always produced good research. But what led to the LLM explosion primarily came from Google Research Mountain View (Transformer), Google Research Seattle (BERT), OpenAI (GPT-3), and various academic labs. During this time DeepMind had a broad research agenda, but my impression is that most resources went towards more traditional deep learning agents in 3D environments, foundational algorithmic research, and games (StarCraft 2). I would provide more detail, but as as an NLP researcher, I did frankly not pay much attention to DeepMind in that era as what was interesting to me just came from elsewhere.

When Google made its first big move into LLMs, its first interesting work did not come out of DeepMind, but rather again Mountain View with PaLM in 2022. Someone with closer connections to Demis at the time can probably explain why the research agenda was what it was, but I lack those connections and DeepMind (even now) has been notoriously tight-lipped since the founding of OpenAI (Demis allegedly sees OpenAI as founded on DeepMind technology by interns and staff walking out on them and remember OpenAI's initial focus on games with Dota 2 compared to DeepMind's with StarCraft 2) and was rather insular compared to Google Research, FAIR, etc. I say "was", but not because DeepMind is now more open, but rather that all industry research outlets are now incredibly tight-lipped after LLMs becoming a product and point of pride among them. At this point, research is held back for maybe even a year before publication or never published at all to deny any perceived advantage to the competition.