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How is Mitoch Shelo lishma ba lishma allowed?

I'm not fully finished with this question as I haven't researched all of my premises, and if someone can point me in the direction of a resource which would stop my question before it starts, that would be great.

One important tenet which I have learned [is ](https://yaelcenter.com/he/home_research/%D7%9E%D7%AA%D7%95%D7%9A-%D7%A9%D7%9C%D7%90-%D7%9C%D7%A9%D7%9E%D7%94-%D7%91%D7%90-%D7%9C%D7%A9%D7%9E%D7%94/)מתוך שלא לשמה בא לשמה, that we are directed to follow Torah and obey mitzvot even if we aren't doing it for the sake of itself but for some other (or no?) reason. Eventually, we will come to do it for the right reason. Something like that.

But if, for example, the mitzvah that I am required to do [requires](https://ph.yhb.org.il/en/02-15-08/#:~:text=The%20halachah%20rules%20that%20mitzvot,the%20kavanah%20that%20accompanies%20it.) intent/kavannah for me to have fulfilled my obligation, and I do it without that proper intent, then it remains unfulfilled. That's not the problem.

What if, in the performance of a mitzvah (without kavannah or any interest in doing the mitzvah) I say Hashem's name? Then I, by following the rule that I do the mitzvah even for the wrong reason, have taken Hashem's name in vain and have transgressed something with its essence steeped in a biblical prohibition. If the name I took in vain was in a bracha (a rabbinic mitzvah) then I have broken a torah level law by (in an empty way) performing a rabbinic one!

So how can we encourage people to do an empty act which will, in some cases, cause the breaking of a Torah level law?