CookingWithGas and Kyla are both right about the pronunciation.
It would be so cool if we could all post phonetic discussions in IPA to avoid confusion. But I don’t know if the characters are all available to all browsers, using Unicode or what. The Character Map in Accessories > System Tools does provide a lot of them.
The low open mid-front vowel you’re talking about (as in dam, damn) is /æ/. It’s true as you said, Kyla, the long vowel in Arabic is usually this sound lengthened [æ:], although this phoneme can also have a different allophone [a:] depending on its consonantal environment. Nitpick: the d is doubled, so it ends the first syllable and also begins the second syllable: sad-DAM.
The first vowel in Saddām is short and the second is long. The sound of the first short a, because of the consonant it follows, is pronounced like uh, so the first syllable sounds about the same as in “sudden.” Followed by “damn.”
In what language?
That’s the right way in what language?
The meaning of Ahmad in Arabic is ‘more praised’. The name Mahmud means ‘praised’, so the comparative form Ahmad means ‘more praised’. Does that make sense? The concept of “praise” is carried by the triliteral root H-M-D which also forms names like Muhammad or Hammād.
The sound of this H does not occur in English. Arabic has two /h/ phonemes: one is the same sound as English /h/. This is the h in Mahdi, for example. But the H in Ahmad, Muhammad, etc. is an unvoiced pharyngeal sound. It is produced by tightly narrowing the pharynx (in the middle of the throat) and exhaling audibly through that narrowed opening, with a sort of hissing sound. Learning how to pronounce this, and its homologous sound ‘ayn, for the first time is an exercise in using speech muscles that one had never been aware of before.
The sound of kh is never correct for Ahmad in Arabic, although in colloquial Uzbek the sound of h followed by a consonant sometimes changes to kh (IPA /x/). For example, the Uzbek word for “thank you” is rahmat (originally the Arabic word for mercy), but is often pronounced “rakhmat.” My co-worker from Samarqand always says “rakhmat” when we talk in Uzbek. I suspect this may be a Russian influence. Russian lacks the sound of /h/ and so substitutes /x/. Khello, khow are you? Students of Central Asian languages come up against Russian mispronunciations all the time. It’s worse than Anglo Americans trying to pronounce “hombre.”