Entering the washroom with a ring on which the name ‘Abd-Allah is written

It is mustahabb to remove anything on
which the name of Allah is written when entering the bathroom (place where
one relieves oneself). If one needs to enter wearing it, then it should be
covered before entering. 

Ibn Qudaamah (may Allah have mercy on him)
said in al-Mughni (1/109): If he wants to enter the washroom and has
something with him on which the name of Allah is mentioned, it is mustahabb
for him to put it down or take it off. If he keeps with him the thing that
he has on which the name of Allah is mentioned, and takes care not to drop
it, or turns the part of the ring on which it is written to face his palm,
there is nothing wrong with that. Ahmad said: If the ring has the name of
Allah on it, he should turn it to face his palm and enter the washroom. This
was the view of Ishaaq and Ibn al-Musayyab, and al-Hasan and Ibn Sireen
granted concessions allowing that. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy
on him) was asked: What is the ruling on entering the washroom with papers
on which the name of Allah is mentioned? 

He replied: It is permissible to enter the
washroom with papers on which the name of Allah is mentioned, so long as
they are in a pocket and are not out in the open; rather they are hidden and
covered. End quote. 

Fataawa min al-Tahaarah,
p. 109 

Based on that, it is permissible for you to
enter the washroom with it, but the writing on the ring should be turned to
the inside, so that it is covered and is not out in the open. 

But it should be noted that if the ring is
an engagement ring, it is not permissible for a Muslim to wear it, because
that is an imitation of the Christians. This has been discussed previously
in the answer to question no.
21441. 

And Allah knows best.