No, the human Y chromosome does not look like a "Y"
A friend brought this 2012 news article about the evolution of the rhesus monkey Y chromosome to my attention. The primary work itself is about characterizing the gene content of the rhesus Y chromosome (a laborious, and necessary task). This particular write-up, however, is slightly frustrating for some of the (wrong) assumptions it makes, but most noticable is the image:
The picture of the “X and Y” chromosomes where the X chromosome, presumably, looks like an X, and the Y chromosome looks like a Y. If this were true, we might then assume that chromosome 1 looks like a “1” and chromsome 22 looks like a “22”. None of these are true.
All human chromosomes, even the six acrocentric chromosomes (13, 14, 15, 21, 22, and Y), look kind of like “X’s” when they are duplicating, having sister chromatids (see this karyotype, a picture of chromosomes: https://www.mun.ca/biology/scarr/Human_Karyotype.html). And none of the chromosomes look like X’s when they are not in the duplication process (see this image from the J. Craig Venter Institute: http://www.jcvi.org/cms/fileadmin/site/research/projects/huref/figure2a.jpg).