The process involved in the specification of identity of a blood vessel endothelial cell. Once specification has taken place, a cell will be committed to differentiate down a specific pathway if left in its normal environment. A blood vessel endothelial cell is an endothelial cell of the vascular tree, which includes blood vessels and lymphatic vessels. [ http://purl.obolibrary.org/obo/CL_0002139 GOC:dgh http://www.ncbi.nlm.nih.gov/pubmed/21521739 ]