Looking at the Jewish view of what 'Hell' is (something spiritual), how are physical places like Sheol, Tophet and Gehinom connected/related to it?
What do their names mean, and how do those meanings reflect what 'Hell' is?
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The Gemara in Eruvin 19a lists several names for Hell:
א"ר יהושע בן לוי ז' שמות יש לגיהנם ואלו הן שאול ואבדון ובאר שחת ובור שאון וטיט היון וצלמות וארץ התחתית...ותו לא והאיכא תפתה
Says R' Yehoshua ben Levi: There are seven names for Gehennom/Hell: She'ol, Avdon, Be'er Shachas, Bor Sha'un, Tit HaYavan, Tzalmaves, and Eretz HaTachtis. ... Are there no more? But there is Tafteh.
According to that Gemara, the name "Gehennom" comes from "גיא שעמוקה (בגיהנם) שהכל יורד לה על עסקי (הנם)" - a deep pit in Hell for those who committed sexual sins (translation follows Rashi). It seems that it could also be related to one of its entrances, discussed earlier in that Gemara, which is between two palm trees in גיא בן הינם, the Valley of Son of Hinnom, a valley in Jerusalem opposite the Jaffa Gate. See my answer to another question of yours on the topic for more on how it got that name.
"She'ol" is derived from the verse in Jonah 2:3, "מִבֶּ֧טֶן שְׁא֛וֹל שִׁוַּ֖עְתִּי שָׁמַ֥עְתָּ קוֹלִֽי" - from the belly of She'ol I cried out, and You heard my voice.1
"Tafteh" is derived from Isaiah 30:33, "כִּֽי־עָר֤וּךְ מֵֽאֶתְמוּל֙ תָּפְתֶּ֔ה" - Tafteh was prepared from yesterday. In context it's very obvious this refers to Hell. JPS translates Tafteh in the verse as Topheth, which I assume is where you got Tophet from. The Gemara also explains that the name is related to the word for being persuaded, מתפתה ("mispaseh" or "mitpateh"), as one who is persuaded by the evil inclination to sin falls into Hell.
1As @DanF was alluding to in the comments (at least, this is how I understood it, hence my reply), the way the Gemara gets this name, and others, out of their respective verses is unclear, and it still doesn't explain why they are called as such. But those questions are for another time.