To the Rabbi:
In the event one experiences an inappropriate thought while reciting Hashem’s Name in tefillah, should one repeat the Name, or continue? Thank you.
No, one should not repeat the Name. Inappropriate thoughts are something that we must try to avoid, but they do not invalidate the tefillah, and the spoken word remains the spoken word.
However, if the Name is part of a pasuk, the pasuk can be recited again with proper intent, and this is fine. If the Name is part of a berachah (Baruch Atah Hashem) it cannot be repeated.