As a general rule, yes loan words are pronounced just as they are written. I say general rule because I have noticed bilingual announcers on the radio who mix English and Japanese do sometimes insert the original pronunciation into their Japanese sentences.
As far as your name is concerned, yes it would be normal to say it as you write it in katakana: When you are trying communicate something on the phone, for example, you don't want people getting distracted with an unpronounceable name, or, off the phone, unwilling to talk to you because they can't say your name properly.
When people meet for the first time names are often an easy talking point, even among Japanese people who ask each other what Kanji they use.