I wouldn't get too nervous about any adjacent meanings in Japan. Not with Sara, anyway. According to the site below, Sara is actually ranked #1348 (out of 5962 possible names) in Japan in a 2023 survey.
ベビーカレンダーが独自で調査・集計した2017年以降に生まれた赤ちゃんの名前データの中から、知りたい名前の順位、よみの順位、漢字の順位がわかる「名前検索」ができます!そのほか、最新の赤ちゃんの名前ランキングや名づけ(名付け)のエピソードをまとめたコンテンツ、名づけニュース、名づけ・命名に関する基礎知識やリアルな体験談など、赤ちゃんの名づけに関する情報が満載です。
If you're going to get worked up about a name, the one to get worked up about would be シミ, which means "stain" in Japanese.
But, we're talking about non-Japanese names on a non-Japanese guy, so everyone will grant him some grace concerning these names. And as long as they are in katakana (and not kanji) I think everyone will know they are names.
サラサミシミ would invite some confusion. Personally, I would arrange the names in vertical order (as you had in your original post) like this;
サラ
サミ
シミ
But depending on the font and the spacing and the skill level of the tattooist, it could indeed end up looking "boxy" and confusing as to whether it should be read horizontally as three words, or vertically as two words. So hopefully your tattooist is Japanese, or has some sensitivity about these things.