Minor detail, LOL
The way I look at it, McLaren needed a new partner (i.e. TAG) to make the Porsche F1 engine happen. Just like TAG Heuer said they needed a partner to bring back the OG F1. They both ended up choosing a partner that required a rebrand of sorts as a key condition of the deal. Seems like Ojjeh/TAG and Fieg/KITH are quite similar in that regard.
What made Ojjeh decide to buy Heuer in the first place I wonder? I'd guess a personal desire by Ojjeh to be associated with Swiss Luxury, similar to his desire to be associated with F1. Can you imagine if Mohamad Al Fayed had changed "Harrods" to "Fayed Harrods" when he purchased the famed luxury department store? That's basically what Ojjeh did.