Maximilian Zerwick insists that εἰς τὸ ὄνομα in Mt 28:19 is being used sensu stricto "to suggest the end and effect of baptism" in the name of the Father, the Son, and the holy spirit: he explicitly connects baptizing with εἰς τὸ ὄνομα. I think Zerwick is also stressing the difference between εἰς and ἐν. See his work Biblical Greek, section 106.
While Zerwick perceives a noticeable lexical distinction between εἰς and ἐν without putting too much emphasis on there being one name for the Father, the Son, and the holy spirit. However, Zerwick does mention the Trinity while articulating the reason for Matthew using εις in 28:19 although I stress that he doesn't argue that all three have the same name.
By "end," I assume that he's referring to the telos of baptism (i.e., goal, purpose, function) and "effect" might be understood as its result (what baptism brings about). One is baptized (Zerwick possibly is arguing) "into" the name of Father, Son and Spirit rather than "in" the name of Father, KTL.
There may not be a major distinction between the two in this case, and for my purposes, it's not all that important.