When my kids were in yeshiva, the school had a policy that they were not allowed to wear kippot that had any writing other than their name, or "Yerushalayim" or something similar. I.e. - no logos like from sports teams or store ads (Yes, they exist. It looks a bit meshugah, but I think it's a clever idea.) The principal considered this "advertising to G-d", in a sense, and this was a Chilul Hashem while in the yeshiva. (I think he didn't want them to wear such kippot even outside of the yeshiva, but he couldn't enforce that.)
Are there any halachic problems with wearing an "advertising" kippah (as described, above)? Is it a chilul Hashem or just considered inappropriate or disrespectful to wear such a kippah in shul or while learning in a yeshiva, Bet Midrash, or for that matter even learning in private at home?