Q. Is an engraved shofar (with outside decorations that are only superficial) kosher? What if it is only my initials? Can I place a label on the shofar with my name?

A. Shulchan Aruch (O.H. 586: 17) rules that it is improper to paint the shofar. Tur quoting Ramban explains that the paint may change the sound of the shofar. (See also Mishna Berura and Kaf Hachaim ibid.) However Remo (ibid.) writes that it is permitted to engrave decorations on the shofar itself. The reason being that even if the sound changes it is from the shofar itself and not due to some extraneous material painted or laid on it. Changing the sound in itself is not detrimental, since all voices from a shofar are acceptable.
However Kaf hachaim (586: 122,) Piskey Teshuvos (ibid.) Zichron Terua (p. 69) and others maintain that it is better not to engrave the shofar at all, since one may accidentally perforate the shofar and disqualify it.
Gluing a label with an identifying name on it, as mentioned before regarding paint, is also improper (Piskey Teshuvos ibid. 10)
Horav Shlomo Miller’s Shlit”a opinion is that it is of utmost importance to maintain the traditional ways of observing mitzvos and not to absorb new meaningless alterations, since there are many reasons why we comply with time-honored traditions. This is especially important in regards to the essential mitzva of shofar. (If someone is afraid that his shofar mat be taken by others, he should place it in a becoming bag with his name on it, as we do with the ta’alis and tefilin)

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a.