Priest with two names

[Ghostwheel]

Do priests ever adopt a new name when they get ordained?

Something that sounds holier, like "Dominick."  Or something like a confirmation name.

Anyone heard of a priest who was known by two different (first) names?

In theory, why would a priest have a different first name on his grave?  And should it probably be considered a birth name, if he does?

[heywood]

Some may have changed their name if they were in a missionary order, for example.
I think most ordained to a diocese did not.
Your priest might just have preferred a different name.
Holier than what? 

[Viktoria]

I think Nuns when they enter a Convent get another name ,leaving the world behind as they take The Veil.
Not sure about Priests though.
Viktoria.

[Ghostwheel]

Holier than what? 

In my case, assuming I am right, and it is the same guy - Lewis.  But Lewis only appears on the grave.  And get this - there is another Dominick buried in it, though I believe he died much later.

As another example, I have found a bishop/archbishop named Edward Dominic Murphy, who seems to have sometimes been called Dominic and sometimes Edward.

I thought Dominick might be a particular name of priests.  Perhaps, of Dominicans.  But Irishgenealogy.ie seems to have a lot of hits for people baptized with the name.

This particular fellow lived during penal times.  I considered the idea it could be an alias, but I just don't think it makes any sense.

And I tried pretty hard to explain it that way.  But he was mentioned in a will as Dominick, one year before he died.

And I really think it must be the same guy.  They were both vicars general.  And what, there is like 1-2 in a diocese?And from what I can tell the guy in the grave was a priest in the same parish at the same time.

Here's the grave, I can find no other certain reference to him as "Lewis."
http://www.enfieldgraveyards.com/Gravestone.aspx?GravestoneID=684

I'm not a 100% sure, but I assume the inscription dates to much later.  Would they say "vicar general", when a bishop was hiding in the same parish in 1704?

[Wexflyer]

Holier than what? 

In my case, assuming I am right, and it is the same guy - Lewis.  But Lewis only appears on the grave.  And get this - there is another Dominick buried in it, though I believe he died much later.

As another example, I have found a bishop/archbishop named Edward Dominic Murphy, who seems to have sometimes been called Dominic and sometimes Edward.

I thought Dominick might be a particular name of priests.  Perhaps, of Dominicans.  But Irishgenealogy.ie seems to have a lot of hits for people baptized with the name.

This particular fellow lived during penal times.  I considered the idea it could be an alias, but I just don't think it makes any sense.

And I tried pretty hard to explain it that way.  But he was mentioned in a will as Dominick, one year before he died.

And I really think it must be the same guy.  They were both vicars general.  And what, there is like 1-2 in a diocese?And from what I can tell the guy in the grave was a priest in the same parish at the same time.

Here's the grave, I can find no other certain reference to him as "Lewis."
http://www.enfieldgraveyards.com/Gravestone.aspx?GravestoneID=684

I'm not a 100% sure, but I assume the inscription dates to much later.  Would they say "vicar general", when a bishop was hiding in the same parish in 1704?

There is a transcription of the memorial inscription on the link you provide.
From it it is clear that there has to be an error somewhere, either in the original inscription, or the transcription.
Viz: According to the transcription, one priest, Lewis, d. 1704, was a brother of Dominick, d. 1785.
That seems highly improbable to me.
Adding to the improbability, you (OP), state that Lewis should himself be Dominick, which would have two brothers of the same name!

So... I would suggest an error in one of the dates, or other wording of the transcription.

In my own experience, I have often found published transcriptions of family memorials to be highly innacurate.

[Wexflyer]

Do priests ever adopt a new name when they get ordained?

Something that sounds holier, like "Dominick."  Or something like a confirmation name.

Anyone heard of a priest who was known by two different (first) names?

In theory, why would a priest have a different first name on his grave?  And should it probably be considered a birth name, if he does?

Secular priests - almost certainly not.
Regular priests - possibly.

[Ghostwheel]

Viz: According to the transcription, one priest, Lewis, d. 1704, was a brother of Dominick, d. 1785

This threw me off at first too.  But I decided, it's probably not literal.

While there are families where multiple brothers were priests, I don't think it was too common.

I'm not sure what "brother" means here exactly.  Perhaps, something like "brother in Christ."  Or that he was some other kind of kin.  (He likely was.)

I am not 100% sure the exact year for the later death can be trusted, but I believe it was much later, and that they weren't siblings.

Dominick is evidenced in 1703, but not on the return of priests in 1704.  Lewis died in 1704, but before the registration date for the return.

Dominick was of a similar age to Lewis.  He was a vicar in 1673 or probably 1672, which would likely mean he was at least 30 back then, and probably older.

There were many Dempsy priests in the parish, over time.  Including a later Lewis and a later Dominick (than the original.)

[Wexflyer]

Viz: According to the transcription, one priest, Lewis, d. 1704, was a brother of Dominick, d. 1785

This threw me off at first too.  But I decided, it's probably not literal.

While there are families where multiple brothers were priests, I don't think it was too common.

I'm not sure what "brother" means here exactly.  Perhaps, something like "brother in Christ."  Or that he was some other kind of kin.  (He likely was.)

I am not 100% sure the exact year for the later death can be trusted, but I believe it was much later, and that they weren't siblings.

Dominick is evidenced in 1703, but not on the return of priests in 1704.  Lewis died in 1704, but before the registration date for the return.

Dominick was of a similar age to Lewis.  He was a vicar in 1673 or probably 1672, which would likely mean he was at least 30 back then, and probably older.

There were many Dempsy priests in the parish, over time.  Including a later Lewis and a later Dominick (than the original.)

My assumption would be that I would need to go read the memorial inscription myself....

[Wexflyer]

One should always consult reference works, when available.
For the Diocese of Kildare and Leighlin, there is a three volume set on the history of the diocese, and all three volumes are available online at:
https://www.askaboutireland.ie/reading-room/digital-book-collection/digital-books-by-county/carlow/comerford-diocese-of-kild/

In Vol. 2 (published 1886), page 67, in the section for the parish of Balyna, I find a transcript of the memorial inscription for Fr. Lewis Dempsy. It is the same wording as on the modern transcript page, linked by OP.

However, the memorial inscription for Fr. Dominick Dempsey,  mentioned immediately afterwards, is simply "Here also lieth Dominck Dempsy".
Nothing else.

Fr. Dominick is also mentioned on page 72 of Vol. 2, as PP of Balyna, with the comment that he is
"interred in the same grave with Lewis Dempsey his predecessor, and very probably, his near relation, at Cadamstown."

Conclusion: additional lines were added to the memorial at some much later date.