Nope, the children will be different than the original if started from seed.
Many people do what is called a "Self" cross, but it would be wrong to call the children the same cultivar as the parents, even if the children are almost identical to the parents.

Thank you, you set me to thinking.Of course, the pollen and ova would not carry all, only some of, the characteristics of the parents, and recessives could pair that weren't paired before and manifest themselves. Thank you

recessives?

Yes Katherine you are correct. The iris may be carrying recessive genes for say plicata pattern. By selfing the bloom, you may produce seedlings in this pattern, if all 4 genes are present. Are you aware that modern Tall Bearded Irises are tetraploid? That is, they carry 4 of each chromosome instead of the usual 2. This makes for more interesting possibilities in hybridising. You are just touching on a very exciting field of interest. Do we have a new hybridiser here?