Let's check this, two wrods are similar to yours :

bee and slim (female)

bee = نحلة = Nahlah...Nah-lah

slim (female) = نحيلة = Nahilah or Naheela...Na-hi(hee)-lah

Hope it's clear and more helpful :)

Rahimah is written رحيمة

becase of the letter " i "

if we remove " i " Rahmah it will be written رحمة

It can't be رحمة....simply because you pronounced it wrong !

ر: Ra
ح: Hi......(this is wrong)

مة: Mah

in the wrods رحمة...letter ح is pronounced just (H) so you make stop on it !

so will be like this :

رح : Rah

مة : mah

While the other word...رحيمة is clear to be :

Ra-hi (hee)-mah

After all you should know that there is something complicated in Arabic language called (Tashkeel..تشكيل) which defines how to pronounce the letter, as the same letter itself might has several sounds !

Sorry to make it long :)

Rahimah

Is the name Rahimah written in Arabic as رحمة or رحيمة?

Why I feel it should be written as رحمة:

It is because Rahimah consists of

ر: Ra
حي: Hi
مة: Mah

Why I feel it should be written as رحيمة:

Hi is pronounced as Hee

Conclusion:

I'll go with رحيمة


Everyone is welcome to share his or her opinion about which one is suitable.

It Pronounced as رحيمة because Hi Pronounced as Hee