Madsen sits next to 4 phonetic neighbors — Madison, Madigan, and Matsen are the closest matches by sound. Most share Madsen's Scandinavian cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"son of Mads (Matthew)"
"that which is believed"
"far-reaching, bringer of completion"
"oak grove, oak tree"
"place of the winding shore"
"He shines"
"slender, narrow"
"faithful, loyal"
"gracious gift"
"modern creative variant of Jason"
"short; courtly"
"son of Jeffrey, son of peace"
"God will teach, God's light"
"God will strengthen"
"heath dweller, one from the heathlands"
"fawn, young deer"
"immense quantity, boundless"
"wooded dune area, hare meadow"
"invented modern name, no established meaning"
"Yahweh is God"
Similar sound: These names share phonetic patterns with Madsen — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Danish origins, giving them the same cultural heritage as Madsen.
Rhythm: Madsen is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.