I'm not knowledgeable about kanji, I can read only hiragana and katakana unfortunately. But, I believe that for names, the kanji are very individual. For example, for 2 names pronounced exactly the same, could be used completely different kanji. So, unless a person is actually given a name in kanji, it is not possible to 'translate' the sound of their name into kanji. And, if they were originally named in kanji and you guess the kanji for the sounds and get it wrong, that could be offensive too ☝
Of course, you can always find out possible kanji representations of Tamika and your fiancee can choose a nice meaning and kanji... any Japanese people out there, would that be an ok thing to do? :?