I prepared a Detailed ROMA-JI table. Some english sounds are shown under the letter . The first one is the preferred option, the second one and the third shows the use in case of coupled "consonant"s and where "consonant" comes as the last letter or shows possible english spelling (a little confusing but I thought it help you somewhat).
    The first thing to do is rewriting your name sound-wise. English language incorporate many origins of words, so there seems to be no rule of pronouncing. Vowels letter "a", "e", "i", "o", "u" usually have some different sounds. And sometimes "y" should be considered as vowel letter.
    "a" is pronounced as 'a', 'ei" and sometimes 'o'. "Andy", "Kate", "Paul".
    "e" is pronounced as 'e', 'i'. "Ted", "Cathleen".
    "i" and "y" are pronounced as 'i', 'ai'. "Alice", "giant", "Abby", "Michael".
    "o" is pronounced as 'o', 'u', 'a'. "Bob", "boot", "foot".    "u" is pronounced as 'u', 'a', 'yu'. "Bush", "Bunny", "Duke"
    And there are combination of vowels that are pronounced differently, "au", 'o-'. "ie" is pronounced as 'i-'.
    Use "capital letter" as a base. And after the vowel word of having short pause like as "Hepburn" and "Bookkeeper", insert '^' when the following consonant is "d", "f", "g", "k", "p", "s", "t". So, "Hepburn" becomes "He^pbA-n" and "Bookkeeper", "Bu^kkI-pA-".
    If the vowel letter has long sound. insert '-' after the vowel letter. If the vowel letter is not pronounced, then neglect it.
    If the vowel letter has slight sound, use "small letter". Thus "Andy", "Kate", "Paul" become 'Andi', 'KEIt', 'PO-l'. "Pat" is rewrited as 'PA^t'. Then regarding consonants followed by a vowel, find corresponding letter in the table.
    '-' should be replaced by , and '^' should be replaced by . 'Andi', 'KEIt', 'PO-l'and 'PA^t" can be transcribed as 'n', 't', 'l' and 't". And "He^pbA-n" and "Bu^kkI-pA-" become and
    "r" followed by "consonant" appears usually as the continuation of the "vowel" before like such as "Carter". It should be considered as long "vowel sound". Thus "Carter" is "Ka-ta-" Continuation of the "vowel" or longer "vowel" is shown by . It makes .
    There are consonants that can not be found in the table. As to "c", replace it with "s" or "k" according to the real pronunciation. As to "q", replacing it with "k" will probably solve the problem.
    As to "ph", it should be replaced by "f". As to "th", it should be replaced with 's' or 'z' according to the real sound. "th" has different sound from 's' or 'z'. But there is no other way.
    As to doubled consonants such as "dd", "gg", "ll","mm","nn", "pp", "rr", "ss", "tt", if the former vowel has accent, then replace the former consonant with '^'. If the former vowel has long sound, replace the former consonant with '-'. "Freddie" becomes "FrE^di-".
    Problem occurs when two different "consonant"s are coupled or a "consonant" comes at the last of a word. In case of coupled "consonants", insert 'u' between the "consonant"s with exception of "d", "t", "n" and "r". "n" not followed by "vowel" or "n" at the end of a word should be considered as independent and you can find "n" sound as . "Anne" becomes 'An' and transcribed as . If the last e of "Anne" is pronounced french-wise, rewrite it as 'Annu'. And it gives . "Andy" becomes
    Thus 'Brown' becomes 'Burowun'. It makes .

    In case of the first "consonant" is "d" and "t", insert 'o" or attach "o" at the end of a word. Thus 'Clint" becomes "Kurinto". It makes .    In english words the last "vowel" like letters such as "Kate" are often not pronounced. They should be omitted. "Kate" becomes "Keit" and next "Keito". It gives . "Pat" becomes . Adding "o" sound at the end of name may sound Italian like name. But there in no way of avoiding it. But japanese know that english words rarely has "o" sound at the end. In case of adding "u" sound at the end of word, Japanese pronounce the last "u" sound slightly, so the result is not so unnatural.
    Some Examples.
"Duke", . "Bryant", .
"Do you like to swim",        .
"This is a flower",      

    I think the description above may be incomplete including several confusions. But at the moment, I finish this page here. For your reference, I prepared a table of transcription examples transcripted in my way. Other people may transcript differently. There is no rule for transcription. In this table, "katakana" is used. But if you prefer "hiragana", I prepared the table for "hiragana".
    There are also prepared Detailed ROMA-JI table in "hiragana".

As to resonants at the end of words or names
    There is no indepent letters for resonants in Japanese letters. Therefore, when a resonant comes at the last of names or words, a vowel should be added. Usually adding "u" is a good solution because the pronunciation of 'u' in japanese pronunciation is rather weak. In this context, usual solution is changing the last "b" to 'bu' (also "v" to 'bu', "c" to 'ku', "d" to 'du' (in reality, japanese like to use 'do' for "d"), "f" (rarely seen) to 'fu", "g" to 'gu', "h" (very rare) to ge ignored, "j" (I never saw "j" at the last of words), "k" to 'ku', "L" to 'ru', "m" to 'mu', "n" to 'n', "p" to 'pu', "q" (I never saw "q" at the last of words), "r" to "ru" (in english words, "r" at the last of a word is something like 'a'), "s" to 'su' (in english 'zu' according to the pronunciation), "t" to 'tu' (in reality, japanese like to use 'to' for "t"), "v" to 'bu' (nowadays more like 'vu' though in case of Russian, 'fu' is thought better), "w" to 'u', "z" to 'zu'. As to the compound resonants, usual solution is changing "th" to 'su', "ts" and "tz" to 'tu'.

    Now I prepared the pages for "Writing english names in kanji (chinese letter). Please visit.