Ottoman actually is a form of Osman. The original name was an Arabic name, Uthman. In Persian and Turkish naming traditions (who, with Islam had adopted some Arabic names like that of Caliph Uthman ibn Affan) this came to be pronounced Osman- in many Arabic dialects short U has a pronounciation O (witness "Muhammad" vs "Mohammed"), and Persian lacked a 'th' sound so they substituted 's' as the closest available sound. Persian-influenced Turks like the Ottomans adopted their names from the Persians rather than directly from Arabic and inherited this.

The form Ottoman derives from an English mispronunciation of the name. Bloom Johnathan in "Islam: A Thousand Year Empire" claims the English word was adopted indirectly through Italian, which would make sense with the time period, but I am not sure where he gathered this.

Etymonline concurs, citing the form as "Ottomano", which would indicate the Italians were adopting it from Arabic (Uthman or Othman) as they did not have the English "TH" sound in their language- in keeping it separate from S, they conflated it with T, but "-tm-" is foreign to Italian phonotactics and so a mirror vowel was inserted to break it up and make it more easily pronouncable to the Italian tongue. In English it was then simply adopted and the Italian nominal ending -o removed, leaving "Ottoman" rather than the original attempt to render "Uthman" or "Othman". This is a pretty standard game of telephone that happens with loanwords, whether they be names or nations- look at how 'Yehoshua' eventually became english 'Joshua'.

The pronunciation "Ottoman" was not universal in English necessary. Apparently Lord Byron preferred the more authentic (but perhaps too arabised) "Othman", for instance.

A final note is that the naming of muslim nations after their dynasties is not necessarily what they called themselves and is a modern tradition. The Ottomans had numerous ways of referring to their own state but generally preferred "The Sublime State" or "The Well Protected Domains" (in Ottoman Turkish, of course). The Mamluks referred to themselves as "The Turkish State", and the Timurids did use a dynastic name but it was not Timurid but actually Gurkani - "Sons in Laws (of Genghis Khan)".

Some groups did use dynastic names, typically things such as "Banu al-(Name)" (The Sons of ___), but some did not and used geographic locations. The modern tradition in English is indeed to generally use dynastic names however.