Franz Otto's father was the parish tailor Carl Ekström.
Bankekinds kyrkoarkiv, Födelse- och dopböcker, SE/VALA/00023/C/5 (1797-1852), bildid: C0015214_00190, sida 364 https://sok.riksarkivet.se/bildvisning/C0015214_00190
Wirf was Franz Otto's soldier name - he was a grenadier.
Östra Ryds kyrkoarkiv, Husförhörslängder, SE/VALA/00488/A I/20 (1871-1875), bildid: C0015091_00170, sida 417 https://sok.riksarkivet.se/bildvisning/C0015091_00170
- he is "Lifgr. Frans Otto Wirf" in the household record.
Franz Otto does not seem to have used the family name Ekström in Sweden because he went straight from home to enrolling as a grenadier - and soldiers were assigned "professional" surnames.
But I assume they all used the family name Ekström in America - his son went by the family name Ekström before he left Sweden and he was the first to leave.
Östra Ryds kyrkoarkiv, Husförhörslängder, SE/VALA/00488/A I/24 (1882-1887), bildid: C0015095_00190, sida 440 https://sok.riksarkivet.se/bildvisning/C0015095_00190
So, looking at the sources, where his father was named Ekström at the time of Frans Otto's birth, and his son (and he himself in America) considered Ekström as their family name, I think it is warranted to use Ekström as Last Name at Birth. He was not born a soldier - and in this case, where he presumably did not use the name Wirf at the end of his life, Wirf would go in the Other Last Names.
If you wish to be kind to us Swedes, please copy-paste the name Ekström to get the Ö. You can use the American spelling Ekstrom as his Current Last Name.