I think you could do this with awk, give this a try:

awk '{print ">"$1"\n"$2}' tab.tsv > seqs.fa

Let me know if that works for you!

Dennis

edit: $1 is your name column and $2 is your sequence column, so switch those if the order is sequence, name.

if first column doesn't have >:

awk -v OFS="\n" '{print ">"$1,$2}' test.txt
sed -e 's/^/>/;s/\t/\n/g' test.txt 
parallel  --colsep '\t'  echo -e '\>{1}\\n{2}'  :::: test.txt