No; apparently tyrd is a northern form and dere a southern, both being the singular command/imperative form of dod.
In case anyone's interested, there's a north/south split with the ti imperative form of "Go!" to: Dos in north Wales, Cer in the south.
I've known people from the valleys to use dewch yma, yet to here dere. It might be certain places in the south for each.
dewch is the plural, which you would use when you're being more polite or when you're speaking to several people at once.
I think that form is used all over Wales, whether they're use tyrd or dere (or possibly something else) for the informal singular.
These days I think they teach:
South: dere (familiar sing.); dewch (polite sing., all plur.)
North: tyrd (familiar sing.); dowch (polite sing., all plur.)
There may be variations on the above but that's basically it.
dowch is actually what I've been hearing in the north; I didn't know that that spelling is also in use.
Croeso! Fyi, for completeness' sake:
formal Welsh: tyred (familiar sing.); dewch (polite sing., all plur.)
That is a frequently used contraction of yma in expressions like this.
Contractions are very often used in spoken Welsh. So much so that some of them have ended up as dictionary words over the years.