I checked the following sources with these results:
1890 Veteran's Census - Index- Allsott, Anson Allstop, Reason
Texas Archives - Confederate Pension Applications Alsup, Sarah E. - Milam Co - William E. Alsup - rej Allsup, William H. - Galveston Co - app #31751 Allsup, Clara H. - Harris Co - app #43148 (widow of above)
Roster of Union Soldiers 1861-1865 Texas: NO variation of name listed
Roster of Confederate Soldiers 1861-1865 (alphabetical- Texas) Alsup, Ludy C.6th Inf Co C Cpl Alsup, R.J. 6th Inf Co C Alsup, T. H. 12th Cav Co D Alsup, W.A. Cav 2nd Bn St Troops Co A Alsup, WIlliam 21st Cav Co D Alsup, William R.6th Inf Co C
Allsop, A.M.15th Inf Co K Allsup, C.S. Cav Bone's Co Allsup, Joseph 7th Cav Co C Allsup, T.H. Cav Waller's Regt Co E Alsop, SamuelCav Baylor's Regt Co D
Not sure if any of this helps or not but that is all I could find.