I've started every meditation session for the past couple years by (1) taking refuge in the three jewels (x3 sometimes) and then (2) generating the two awakening minds (at least formally. Too formally and not enough lively, perhaps).

But strangely enough, no, I would not identify myself as buddhist.

Sometimes i'll change the wordings to something less sanskrity, like, "I take refuge in awakening/the absolute/the truth/reality, in the people who have shown the way, and in all those who are engaged on the path towards this realization." You feel the spirit

I formally became a Buddhist by taking the five precepts at a Zen temple. It had nothing to do with respecting any formal institution or ideology or religion, it was just a way of committing yourself to following to the five precepts because you believed it would help your practice to avoid conduct that would cause mental turbulence. It was pragmatic dharma.

I don't indentify as a Buddhist. I thought about it briefly after having my big A&P experience and decided to wait before making any decisions. I've decided that it would just not be that meaningful or helpful for me. I already have identities that I think are healthy and doing their job. I don't see the need to add another one.