For the Rambam (based on the mishna in Sanhedrin 7:5) the formal law of blasphemy only applies to the names of God that are forbidden to be erased. The english name "God" is not one of those. Doesn't mean it is a good idea to curse it - just that it is not the subject of the halachic prohibition of blasphemy or cursing God's name.
The Rambam in MT Avodat Kochavim 2:7 writes
These are the laws which govern a blasphemer: A blasphemer is not
liable to be stoned to death until he states God's unique name, which
possesses four letters: א-ד-נ-י, and curses that name with one of the
names of God which are forbidden to be erased [...]
One is obligated to be stoned to death for blaspheming God's unique
name. [Should he blaspheme] the other names for God, he [transgresses]
There are those who state that one is liable [for execution] only when
one blasphemes the name י-ה-ו-ה. I, however, maintain that one should
be stoned to death in both instances.
and in Avodat Kochavim 2:9
Should a person curse God's name with the name of a false god, the
zealous may strike him and slay him. If the zealous do not slay him
and he is brought to court, he is not [condemned to] be stoned. [That
punishment is administered] only when one curses God's name with
another one of His unique names.
In MT Yesodei HaTorah 6:2 he defines the names not to be erased as
There are seven names [for God]:
a) The name which is written Yud-Hey-Vav-Hey. This is [referred to as
God's] explicit name and is [also] written Alef-Daled-Nun-Yud.
b) [The name] El;
c) [The name] Elo'ah;
d) [The name] Elohim;
e) [The name] Elohai;
f) [The name] Shaddai;
g) [The name] Tz'vaot;
Whoever erases even one letter from [any of] these seven names is
[liable for] lashes.
As myjewishlearning writes
To insult the Torah or Moses, the other prophets, or the sages of
Israel is also held to be a serious offense but this is, at the most,
an extension of the original blasphemy law and is not covered by the
death penalty, even in theory. [...]
There is hardly any evidence that trials for blasphemy took place
among Jews in post-biblical times.